__tree 102 KB
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 2721 2722 2723 2724 2725 2726 2727 2728 2729 2730 2731 2732 2733 2734 2735 2736 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 2769 2770 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 2834 2835 2836 2837 2838 2839 2840 2841 2842 2843 2844 2845 2846
// -*- C++ -*-
//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP___TREE
#define _LIBCPP___TREE

#include <__config>
#include <iterator>
#include <memory>
#include <stdexcept>
#include <algorithm>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#pragma GCC system_header
#endif

_LIBCPP_PUSH_MACROS
#include <__undef_macros>


_LIBCPP_BEGIN_NAMESPACE_STD

#if defined(__GNUC__) && !defined(__clang__) // gcc.gnu.org/PR37804
template <class, class, class, class> class _LIBCPP_TEMPLATE_VIS map;
template <class, class, class, class> class _LIBCPP_TEMPLATE_VIS multimap;
template <class, class, class> class _LIBCPP_TEMPLATE_VIS set;
template <class, class, class> class _LIBCPP_TEMPLATE_VIS multiset;
#endif

template <class _Tp, class _Compare, class _Allocator> class __tree;
template <class _Tp, class _NodePtr, class _DiffType>
    class _LIBCPP_TEMPLATE_VIS __tree_iterator;
template <class _Tp, class _ConstNodePtr, class _DiffType>
    class _LIBCPP_TEMPLATE_VIS __tree_const_iterator;

template <class _Pointer> class __tree_end_node;
template <class _VoidPtr> class __tree_node_base;
template <class _Tp, class _VoidPtr> class __tree_node;

template <class _Key, class _Value>
struct __value_type;

template <class _Allocator> class __map_node_destructor;
template <class _TreeIterator> class _LIBCPP_TEMPLATE_VIS __map_iterator;
template <class _TreeIterator> class _LIBCPP_TEMPLATE_VIS __map_const_iterator;

/*

_NodePtr algorithms

The algorithms taking _NodePtr are red black tree algorithms.  Those
algorithms taking a parameter named __root should assume that __root
points to a proper red black tree (unless otherwise specified).

Each algorithm herein assumes that __root->__parent_ points to a non-null
structure which has a member __left_ which points back to __root.  No other
member is read or written to at __root->__parent_.

__root->__parent_ will be referred to below (in comments only) as end_node.
end_node->__left_ is an externably accessible lvalue for __root, and can be
changed by node insertion and removal (without explicit reference to end_node).

All nodes (with the exception of end_node), even the node referred to as
__root, have a non-null __parent_ field.

*/

// Returns:  true if __x is a left child of its parent, else false
// Precondition:  __x != nullptr.
template <class _NodePtr>
inline _LIBCPP_INLINE_VISIBILITY
bool
__tree_is_left_child(_NodePtr __x) _NOEXCEPT
{
    return __x == __x->__parent_->__left_;
}

// Determines if the subtree rooted at __x is a proper red black subtree.  If
//    __x is a proper subtree, returns the black height (null counts as 1).  If
//    __x is an improper subtree, returns 0.
template <class _NodePtr>
unsigned
__tree_sub_invariant(_NodePtr __x)
{
    if (__x == nullptr)
        return 1;
    // parent consistency checked by caller
    // check __x->__left_ consistency
    if (__x->__left_ != nullptr && __x->__left_->__parent_ != __x)
        return 0;
    // check __x->__right_ consistency
    if (__x->__right_ != nullptr && __x->__right_->__parent_ != __x)
        return 0;
    // check __x->__left_ != __x->__right_ unless both are nullptr
    if (__x->__left_ == __x->__right_ && __x->__left_ != nullptr)
        return 0;
    // If this is red, neither child can be red
    if (!__x->__is_black_)
    {
        if (__x->__left_ && !__x->__left_->__is_black_)
            return 0;
        if (__x->__right_ && !__x->__right_->__is_black_)
            return 0;
    }
    unsigned __h = __tree_sub_invariant(__x->__left_);
    if (__h == 0)
        return 0;  // invalid left subtree
    if (__h != __tree_sub_invariant(__x->__right_))
        return 0;  // invalid or different height right subtree
    return __h + __x->__is_black_;  // return black height of this node
}

// Determines if the red black tree rooted at __root is a proper red black tree.
//    __root == nullptr is a proper tree.  Returns true is __root is a proper
//    red black tree, else returns false.
template <class _NodePtr>
bool
__tree_invariant(_NodePtr __root)
{
    if (__root == nullptr)
        return true;
    // check __x->__parent_ consistency
    if (__root->__parent_ == nullptr)
        return false;
    if (!__tree_is_left_child(__root))
        return false;
    // root must be black
    if (!__root->__is_black_)
        return false;
    // do normal node checks
    return __tree_sub_invariant(__root) != 0;
}

// Returns:  pointer to the left-most node under __x.
// Precondition:  __x != nullptr.
template <class _NodePtr>
inline _LIBCPP_INLINE_VISIBILITY
_NodePtr
__tree_min(_NodePtr __x) _NOEXCEPT
{
    while (__x->__left_ != nullptr)
        __x = __x->__left_;
    return __x;
}

// Returns:  pointer to the right-most node under __x.
// Precondition:  __x != nullptr.
template <class _NodePtr>
inline _LIBCPP_INLINE_VISIBILITY
_NodePtr
__tree_max(_NodePtr __x) _NOEXCEPT
{
    while (__x->__right_ != nullptr)
        __x = __x->__right_;
    return __x;
}

// Returns:  pointer to the next in-order node after __x.
// Precondition:  __x != nullptr.
template <class _NodePtr>
_NodePtr
__tree_next(_NodePtr __x) _NOEXCEPT
{
    if (__x->__right_ != nullptr)
        return __tree_min(__x->__right_);
    while (!__tree_is_left_child(__x))
        __x = __x->__parent_unsafe();
    return __x->__parent_unsafe();
}

template <class _EndNodePtr, class _NodePtr>
inline _LIBCPP_INLINE_VISIBILITY
_EndNodePtr
__tree_next_iter(_NodePtr __x) _NOEXCEPT
{
    if (__x->__right_ != nullptr)
        return static_cast<_EndNodePtr>(__tree_min(__x->__right_));
    while (!__tree_is_left_child(__x))
        __x = __x->__parent_unsafe();
    return static_cast<_EndNodePtr>(__x->__parent_);
}

// Returns:  pointer to the previous in-order node before __x.
// Precondition:  __x != nullptr.
// Note: __x may be the end node.
template <class _NodePtr, class _EndNodePtr>
inline _LIBCPP_INLINE_VISIBILITY
_NodePtr
__tree_prev_iter(_EndNodePtr __x) _NOEXCEPT
{
    if (__x->__left_ != nullptr)
        return __tree_max(__x->__left_);
    _NodePtr __xx = static_cast<_NodePtr>(__x);
    while (__tree_is_left_child(__xx))
        __xx = __xx->__parent_unsafe();
    return __xx->__parent_unsafe();
}

// Returns:  pointer to a node which has no children
// Precondition:  __x != nullptr.
template <class _NodePtr>
_NodePtr
__tree_leaf(_NodePtr __x) _NOEXCEPT
{
    while (true)
    {
        if (__x->__left_ != nullptr)
        {
            __x = __x->__left_;
            continue;
        }
        if (__x->__right_ != nullptr)
        {
            __x = __x->__right_;
            continue;
        }
        break;
    }
    return __x;
}

// Effects:  Makes __x->__right_ the subtree root with __x as its left child
//           while preserving in-order order.
// Precondition:  __x->__right_ != nullptr
template <class _NodePtr>
void
__tree_left_rotate(_NodePtr __x) _NOEXCEPT
{
    _NodePtr __y = __x->__right_;
    __x->__right_ = __y->__left_;
    if (__x->__right_ != nullptr)
        __x->__right_->__set_parent(__x);
    __y->__parent_ = __x->__parent_;
    if (__tree_is_left_child(__x))
        __x->__parent_->__left_ = __y;
    else
        __x->__parent_unsafe()->__right_ = __y;
    __y->__left_ = __x;
    __x->__set_parent(__y);
}

// Effects:  Makes __x->__left_ the subtree root with __x as its right child
//           while preserving in-order order.
// Precondition:  __x->__left_ != nullptr
template <class _NodePtr>
void
__tree_right_rotate(_NodePtr __x) _NOEXCEPT
{
    _NodePtr __y = __x->__left_;
    __x->__left_ = __y->__right_;
    if (__x->__left_ != nullptr)
        __x->__left_->__set_parent(__x);
    __y->__parent_ = __x->__parent_;
    if (__tree_is_left_child(__x))
        __x->__parent_->__left_ = __y;
    else
        __x->__parent_unsafe()->__right_ = __y;
    __y->__right_ = __x;
    __x->__set_parent(__y);
}

// Effects:  Rebalances __root after attaching __x to a leaf.
// Precondition:  __root != nulptr && __x != nullptr.
//                __x has no children.
//                __x == __root or == a direct or indirect child of __root.
//                If __x were to be unlinked from __root (setting __root to
//                  nullptr if __root == __x), __tree_invariant(__root) == true.
// Postcondition: __tree_invariant(end_node->__left_) == true.  end_node->__left_
//                may be different than the value passed in as __root.
template <class _NodePtr>
void
__tree_balance_after_insert(_NodePtr __root, _NodePtr __x) _NOEXCEPT
{
    __x->__is_black_ = __x == __root;
    while (__x != __root && !__x->__parent_unsafe()->__is_black_)
    {
        // __x->__parent_ != __root because __x->__parent_->__is_black == false
        if (__tree_is_left_child(__x->__parent_unsafe()))
        {
            _NodePtr __y = __x->__parent_unsafe()->__parent_unsafe()->__right_;
            if (__y != nullptr && !__y->__is_black_)
            {
                __x = __x->__parent_unsafe();
                __x->__is_black_ = true;
                __x = __x->__parent_unsafe();
                __x->__is_black_ = __x == __root;
                __y->__is_black_ = true;
            }
            else
            {
                if (!__tree_is_left_child(__x))
                {
                    __x = __x->__parent_unsafe();
                    __tree_left_rotate(__x);
                }
                __x = __x->__parent_unsafe();
                __x->__is_black_ = true;
                __x = __x->__parent_unsafe();
                __x->__is_black_ = false;
                __tree_right_rotate(__x);
                break;
            }
        }
        else
        {
            _NodePtr __y = __x->__parent_unsafe()->__parent_->__left_;
            if (__y != nullptr && !__y->__is_black_)
            {
                __x = __x->__parent_unsafe();
                __x->__is_black_ = true;
                __x = __x->__parent_unsafe();
                __x->__is_black_ = __x == __root;
                __y->__is_black_ = true;
            }
            else
            {
                if (__tree_is_left_child(__x))
                {
                    __x = __x->__parent_unsafe();
                    __tree_right_rotate(__x);
                }
                __x = __x->__parent_unsafe();
                __x->__is_black_ = true;
                __x = __x->__parent_unsafe();
                __x->__is_black_ = false;
                __tree_left_rotate(__x);
                break;
            }
        }
    }
}

// Precondition:  __root != nullptr && __z != nullptr.
//                __tree_invariant(__root) == true.
//                __z == __root or == a direct or indirect child of __root.
// Effects:  unlinks __z from the tree rooted at __root, rebalancing as needed.
// Postcondition: __tree_invariant(end_node->__left_) == true && end_node->__left_
//                nor any of its children refer to __z.  end_node->__left_
//                may be different than the value passed in as __root.
template <class _NodePtr>
void
__tree_remove(_NodePtr __root, _NodePtr __z) _NOEXCEPT
{
    // __z will be removed from the tree.  Client still needs to destruct/deallocate it
    // __y is either __z, or if __z has two children, __tree_next(__z).
    // __y will have at most one child.
    // __y will be the initial hole in the tree (make the hole at a leaf)
    _NodePtr __y = (__z->__left_ == nullptr || __z->__right_ == nullptr) ?
                    __z : __tree_next(__z);
    // __x is __y's possibly null single child
    _NodePtr __x = __y->__left_ != nullptr ? __y->__left_ : __y->__right_;
    // __w is __x's possibly null uncle (will become __x's sibling)
    _NodePtr __w = nullptr;
    // link __x to __y's parent, and find __w
    if (__x != nullptr)
        __x->__parent_ = __y->__parent_;
    if (__tree_is_left_child(__y))
    {
        __y->__parent_->__left_ = __x;
        if (__y != __root)
            __w = __y->__parent_unsafe()->__right_;
        else
            __root = __x;  // __w == nullptr
    }
    else
    {
        __y->__parent_unsafe()->__right_ = __x;
        // __y can't be root if it is a right child
        __w = __y->__parent_->__left_;
    }
    bool __removed_black = __y->__is_black_;
    // If we didn't remove __z, do so now by splicing in __y for __z,
    //    but copy __z's color.  This does not impact __x or __w.
    if (__y != __z)
    {
        // __z->__left_ != nulptr but __z->__right_ might == __x == nullptr
        __y->__parent_ = __z->__parent_;
        if (__tree_is_left_child(__z))
            __y->__parent_->__left_ = __y;
        else
            __y->__parent_unsafe()->__right_ = __y;
        __y->__left_ = __z->__left_;
        __y->__left_->__set_parent(__y);
        __y->__right_ = __z->__right_;
        if (__y->__right_ != nullptr)
            __y->__right_->__set_parent(__y);
        __y->__is_black_ = __z->__is_black_;
        if (__root == __z)
            __root = __y;
    }
    // There is no need to rebalance if we removed a red, or if we removed
    //     the last node.
    if (__removed_black && __root != nullptr)
    {
        // Rebalance:
        // __x has an implicit black color (transferred from the removed __y)
        //    associated with it, no matter what its color is.
        // If __x is __root (in which case it can't be null), it is supposed
        //    to be black anyway, and if it is doubly black, then the double
        //    can just be ignored.
        // If __x is red (in which case it can't be null), then it can absorb
        //    the implicit black just by setting its color to black.
        // Since __y was black and only had one child (which __x points to), __x
        //   is either red with no children, else null, otherwise __y would have
        //   different black heights under left and right pointers.
        // if (__x == __root || __x != nullptr && !__x->__is_black_)
        if (__x != nullptr)
            __x->__is_black_ = true;
        else
        {
            //  Else __x isn't root, and is "doubly black", even though it may
            //     be null.  __w can not be null here, else the parent would
            //     see a black height >= 2 on the __x side and a black height
            //     of 1 on the __w side (__w must be a non-null black or a red
            //     with a non-null black child).
            while (true)
            {
                if (!__tree_is_left_child(__w))  // if x is left child
                {
                    if (!__w->__is_black_)
                    {
                        __w->__is_black_ = true;
                        __w->__parent_unsafe()->__is_black_ = false;
                        __tree_left_rotate(__w->__parent_unsafe());
                        // __x is still valid
                        // reset __root only if necessary
                        if (__root == __w->__left_)
                            __root = __w;
                        // reset sibling, and it still can't be null
                        __w = __w->__left_->__right_;
                    }
                    // __w->__is_black_ is now true, __w may have null children
                    if ((__w->__left_  == nullptr || __w->__left_->__is_black_) &&
                        (__w->__right_ == nullptr || __w->__right_->__is_black_))
                    {
                        __w->__is_black_ = false;
                        __x = __w->__parent_unsafe();
                        // __x can no longer be null
                        if (__x == __root || !__x->__is_black_)
                        {
                            __x->__is_black_ = true;
                            break;
                        }
                        // reset sibling, and it still can't be null
                        __w = __tree_is_left_child(__x) ?
                                    __x->__parent_unsafe()->__right_ :
                                    __x->__parent_->__left_;
                        // continue;
                    }
                    else  // __w has a red child
                    {
                        if (__w->__right_ == nullptr || __w->__right_->__is_black_)
                        {
                            // __w left child is non-null and red
                            __w->__left_->__is_black_ = true;
                            __w->__is_black_ = false;
                            __tree_right_rotate(__w);
                            // __w is known not to be root, so root hasn't changed
                            // reset sibling, and it still can't be null
                            __w = __w->__parent_unsafe();
                        }
                        // __w has a right red child, left child may be null
                        __w->__is_black_ = __w->__parent_unsafe()->__is_black_;
                        __w->__parent_unsafe()->__is_black_ = true;
                        __w->__right_->__is_black_ = true;
                        __tree_left_rotate(__w->__parent_unsafe());
                        break;
                    }
                }
                else
                {
                    if (!__w->__is_black_)
                    {
                        __w->__is_black_ = true;
                        __w->__parent_unsafe()->__is_black_ = false;
                        __tree_right_rotate(__w->__parent_unsafe());
                        // __x is still valid
                        // reset __root only if necessary
                        if (__root == __w->__right_)
                            __root = __w;
                        // reset sibling, and it still can't be null
                        __w = __w->__right_->__left_;
                    }
                    // __w->__is_black_ is now true, __w may have null children
                    if ((__w->__left_  == nullptr || __w->__left_->__is_black_) &&
                        (__w->__right_ == nullptr || __w->__right_->__is_black_))
                    {
                        __w->__is_black_ = false;
                        __x = __w->__parent_unsafe();
                        // __x can no longer be null
                        if (!__x->__is_black_ || __x == __root)
                        {
                            __x->__is_black_ = true;
                            break;
                        }
                        // reset sibling, and it still can't be null
                        __w = __tree_is_left_child(__x) ?
                                    __x->__parent_unsafe()->__right_ :
                                    __x->__parent_->__left_;
                        // continue;
                    }
                    else  // __w has a red child
                    {
                        if (__w->__left_ == nullptr || __w->__left_->__is_black_)
                        {
                            // __w right child is non-null and red
                            __w->__right_->__is_black_ = true;
                            __w->__is_black_ = false;
                            __tree_left_rotate(__w);
                            // __w is known not to be root, so root hasn't changed
                            // reset sibling, and it still can't be null
                            __w = __w->__parent_unsafe();
                        }
                        // __w has a left red child, right child may be null
                        __w->__is_black_ = __w->__parent_unsafe()->__is_black_;
                        __w->__parent_unsafe()->__is_black_ = true;
                        __w->__left_->__is_black_ = true;
                        __tree_right_rotate(__w->__parent_unsafe());
                        break;
                    }
                }
            }
        }
    }
}

// node traits


#ifndef _LIBCPP_CXX03_LANG
template <class _Tp>
struct __is_tree_value_type_imp : false_type {};

template <class _Key, class _Value>
struct __is_tree_value_type_imp<__value_type<_Key, _Value>> : true_type {};

template <class ..._Args>
struct __is_tree_value_type : false_type {};

template <class _One>
struct __is_tree_value_type<_One> : __is_tree_value_type_imp<typename __uncvref<_One>::type> {};
#endif

template <class _Tp>
struct __tree_key_value_types {
  typedef _Tp key_type;
  typedef _Tp __node_value_type;
  typedef _Tp __container_value_type;
  static const bool __is_map = false;

  _LIBCPP_INLINE_VISIBILITY
  static key_type const& __get_key(_Tp const& __v) {
    return __v;
  }
  _LIBCPP_INLINE_VISIBILITY
  static __container_value_type const& __get_value(__node_value_type const& __v) {
    return __v;
  }
  _LIBCPP_INLINE_VISIBILITY
  static __container_value_type* __get_ptr(__node_value_type& __n) {
    return _VSTD::addressof(__n);
  }
#ifndef _LIBCPP_CXX03_LANG
  _LIBCPP_INLINE_VISIBILITY
  static __container_value_type&& __move(__node_value_type& __v) {
    return _VSTD::move(__v);
  }
#endif
};

template <class _Key, class _Tp>
struct __tree_key_value_types<__value_type<_Key, _Tp> > {
  typedef _Key                                         key_type;
  typedef _Tp                                          mapped_type;
  typedef __value_type<_Key, _Tp>                      __node_value_type;
  typedef pair<const _Key, _Tp>                        __container_value_type;
  typedef __container_value_type                       __map_value_type;
  static const bool __is_map = true;

  _LIBCPP_INLINE_VISIBILITY
  static key_type const&
  __get_key(__node_value_type const& __t) {
    return __t.__get_value().first;
  }

  template <class _Up>
  _LIBCPP_INLINE_VISIBILITY
  static typename enable_if<__is_same_uncvref<_Up, __container_value_type>::value,
      key_type const&>::type
  __get_key(_Up& __t) {
    return __t.first;
  }

  _LIBCPP_INLINE_VISIBILITY
  static __container_value_type const&
  __get_value(__node_value_type const& __t) {
    return __t.__get_value();
  }

  template <class _Up>
  _LIBCPP_INLINE_VISIBILITY
  static typename enable_if<__is_same_uncvref<_Up, __container_value_type>::value,
      __container_value_type const&>::type
  __get_value(_Up& __t) {
    return __t;
  }

  _LIBCPP_INLINE_VISIBILITY
  static __container_value_type* __get_ptr(__node_value_type& __n) {
    return _VSTD::addressof(__n.__get_value());
  }

#ifndef _LIBCPP_CXX03_LANG
  _LIBCPP_INLINE_VISIBILITY
  static pair<key_type&&, mapped_type&&> __move(__node_value_type& __v) {
    return __v.__move();
  }
#endif
};

template <class _VoidPtr>
struct __tree_node_base_types {
  typedef _VoidPtr                                               __void_pointer;

  typedef __tree_node_base<__void_pointer>                      __node_base_type;
  typedef typename __rebind_pointer<_VoidPtr, __node_base_type>::type
                                                             __node_base_pointer;

  typedef __tree_end_node<__node_base_pointer>                  __end_node_type;
  typedef typename __rebind_pointer<_VoidPtr, __end_node_type>::type
                                                             __end_node_pointer;
#if defined(_LIBCPP_ABI_TREE_REMOVE_NODE_POINTER_UB)
  typedef __end_node_pointer __parent_pointer;
#else
  typedef typename conditional<
      is_pointer<__end_node_pointer>::value,
        __end_node_pointer,
        __node_base_pointer>::type __parent_pointer;
#endif

private:
  static_assert((is_same<typename pointer_traits<_VoidPtr>::element_type, void>::value),
                  "_VoidPtr does not point to unqualified void type");
};

template <class _Tp, class _AllocPtr, class _KVTypes = __tree_key_value_types<_Tp>,
         bool = _KVTypes::__is_map>
struct __tree_map_pointer_types {};

template <class _Tp, class _AllocPtr, class _KVTypes>
struct __tree_map_pointer_types<_Tp, _AllocPtr, _KVTypes, true> {
  typedef typename _KVTypes::__map_value_type   _Mv;
  typedef typename __rebind_pointer<_AllocPtr, _Mv>::type
                                                       __map_value_type_pointer;
  typedef typename __rebind_pointer<_AllocPtr, const _Mv>::type
                                                 __const_map_value_type_pointer;
};

template <class _NodePtr, class _NodeT = typename pointer_traits<_NodePtr>::element_type>
struct __tree_node_types;

template <class _NodePtr, class _Tp, class _VoidPtr>
struct __tree_node_types<_NodePtr, __tree_node<_Tp, _VoidPtr> >
    : public __tree_node_base_types<_VoidPtr>,
             __tree_key_value_types<_Tp>,
             __tree_map_pointer_types<_Tp, _VoidPtr>
{
  typedef __tree_node_base_types<_VoidPtr> __base;
  typedef __tree_key_value_types<_Tp>      __key_base;
  typedef __tree_map_pointer_types<_Tp, _VoidPtr> __map_pointer_base;
public:

  typedef typename pointer_traits<_NodePtr>::element_type       __node_type;
  typedef _NodePtr                                              __node_pointer;

  typedef _Tp                                                 __node_value_type;
  typedef typename __rebind_pointer<_VoidPtr, __node_value_type>::type
                                                      __node_value_type_pointer;
  typedef typename __rebind_pointer<_VoidPtr, const __node_value_type>::type
                                                __const_node_value_type_pointer;
#if defined(_LIBCPP_ABI_TREE_REMOVE_NODE_POINTER_UB)
  typedef typename __base::__end_node_pointer __iter_pointer;
#else
  typedef typename conditional<
      is_pointer<__node_pointer>::value,
        typename __base::__end_node_pointer,
        __node_pointer>::type __iter_pointer;
#endif
private:
    static_assert(!is_const<__node_type>::value,
                "_NodePtr should never be a pointer to const");
    static_assert((is_same<typename __rebind_pointer<_VoidPtr, __node_type>::type,
                          _NodePtr>::value), "_VoidPtr does not rebind to _NodePtr.");
};

template <class _ValueTp, class _VoidPtr>
struct __make_tree_node_types {
  typedef typename __rebind_pointer<_VoidPtr, __tree_node<_ValueTp, _VoidPtr> >::type
                                                                        _NodePtr;
  typedef __tree_node_types<_NodePtr> type;
};

// node

template <class _Pointer>
class __tree_end_node
{
public:
    typedef _Pointer pointer;
    pointer __left_;

    _LIBCPP_INLINE_VISIBILITY
    __tree_end_node() _NOEXCEPT : __left_() {}
};

template <class _VoidPtr>
class __tree_node_base
    : public __tree_node_base_types<_VoidPtr>::__end_node_type
{
    typedef __tree_node_base_types<_VoidPtr> _NodeBaseTypes;

public:
    typedef typename _NodeBaseTypes::__node_base_pointer pointer;
    typedef typename _NodeBaseTypes::__parent_pointer __parent_pointer;

    pointer          __right_;
    __parent_pointer __parent_;
    bool __is_black_;

    _LIBCPP_INLINE_VISIBILITY
    pointer __parent_unsafe() const { return static_cast<pointer>(__parent_);}

    _LIBCPP_INLINE_VISIBILITY
    void __set_parent(pointer __p) {
        __parent_ = static_cast<__parent_pointer>(__p);
    }

private:
  ~__tree_node_base() _LIBCPP_EQUAL_DELETE;
  __tree_node_base(__tree_node_base const&) _LIBCPP_EQUAL_DELETE;
  __tree_node_base& operator=(__tree_node_base const&) _LIBCPP_EQUAL_DELETE;
};

template <class _Tp, class _VoidPtr>
class __tree_node
    : public __tree_node_base<_VoidPtr>
{
public:
    typedef _Tp __node_value_type;

    __node_value_type __value_;

private:
  ~__tree_node() _LIBCPP_EQUAL_DELETE;
  __tree_node(__tree_node const&) _LIBCPP_EQUAL_DELETE;
  __tree_node& operator=(__tree_node const&) _LIBCPP_EQUAL_DELETE;
};


template <class _Allocator>
class __tree_node_destructor
{
    typedef _Allocator                                      allocator_type;
    typedef allocator_traits<allocator_type>                __alloc_traits;

public:
    typedef typename __alloc_traits::pointer                pointer;
private:
    typedef __tree_node_types<pointer> _NodeTypes;
    allocator_type& __na_;


public:
    bool __value_constructed;


    __tree_node_destructor(const __tree_node_destructor &) = default;
    __tree_node_destructor& operator=(const __tree_node_destructor&) = delete;

    _LIBCPP_INLINE_VISIBILITY
    explicit __tree_node_destructor(allocator_type& __na, bool __val = false) _NOEXCEPT
        : __na_(__na),
          __value_constructed(__val)
        {}

    _LIBCPP_INLINE_VISIBILITY
    void operator()(pointer __p) _NOEXCEPT
    {
        if (__value_constructed)
            __alloc_traits::destroy(__na_, _NodeTypes::__get_ptr(__p->__value_));
        if (__p)
            __alloc_traits::deallocate(__na_, __p, 1);
    }

    template <class> friend class __map_node_destructor;
};

#if _LIBCPP_STD_VER > 14
template <class _NodeType, class _Alloc>
struct __generic_container_node_destructor;
template <class _Tp, class _VoidPtr, class _Alloc>
struct __generic_container_node_destructor<__tree_node<_Tp, _VoidPtr>, _Alloc>
    : __tree_node_destructor<_Alloc>
{
    using __tree_node_destructor<_Alloc>::__tree_node_destructor;
};
#endif

template <class _Tp, class _NodePtr, class _DiffType>
class _LIBCPP_TEMPLATE_VIS __tree_iterator
{
    typedef __tree_node_types<_NodePtr>                     _NodeTypes;
    typedef _NodePtr                                        __node_pointer;
    typedef typename _NodeTypes::__node_base_pointer        __node_base_pointer;
    typedef typename _NodeTypes::__end_node_pointer         __end_node_pointer;
    typedef typename _NodeTypes::__iter_pointer             __iter_pointer;
    typedef pointer_traits<__node_pointer> __pointer_traits;

    __iter_pointer __ptr_;

public:
    typedef bidirectional_iterator_tag                     iterator_category;
    typedef _Tp                                            value_type;
    typedef _DiffType                                      difference_type;
    typedef value_type&                                    reference;
    typedef typename _NodeTypes::__node_value_type_pointer pointer;

    _LIBCPP_INLINE_VISIBILITY __tree_iterator() _NOEXCEPT
#if _LIBCPP_STD_VER > 11
    : __ptr_(nullptr)
#endif
    {}

    _LIBCPP_INLINE_VISIBILITY reference operator*() const
        {return __get_np()->__value_;}
    _LIBCPP_INLINE_VISIBILITY pointer operator->() const
        {return pointer_traits<pointer>::pointer_to(__get_np()->__value_);}

    _LIBCPP_INLINE_VISIBILITY
    __tree_iterator& operator++() {
      __ptr_ = static_cast<__iter_pointer>(
          __tree_next_iter<__end_node_pointer>(static_cast<__node_base_pointer>(__ptr_)));
      return *this;
    }
    _LIBCPP_INLINE_VISIBILITY
    __tree_iterator operator++(int)
        {__tree_iterator __t(*this); ++(*this); return __t;}

    _LIBCPP_INLINE_VISIBILITY
    __tree_iterator& operator--() {
      __ptr_ = static_cast<__iter_pointer>(__tree_prev_iter<__node_base_pointer>(
          static_cast<__end_node_pointer>(__ptr_)));
      return *this;
    }
    _LIBCPP_INLINE_VISIBILITY
    __tree_iterator operator--(int)
        {__tree_iterator __t(*this); --(*this); return __t;}

    friend _LIBCPP_INLINE_VISIBILITY
        bool operator==(const __tree_iterator& __x, const __tree_iterator& __y)
        {return __x.__ptr_ == __y.__ptr_;}
    friend _LIBCPP_INLINE_VISIBILITY
        bool operator!=(const __tree_iterator& __x, const __tree_iterator& __y)
        {return !(__x == __y);}

private:
    _LIBCPP_INLINE_VISIBILITY
    explicit __tree_iterator(__node_pointer __p) _NOEXCEPT : __ptr_(__p) {}
    _LIBCPP_INLINE_VISIBILITY
    explicit __tree_iterator(__end_node_pointer __p) _NOEXCEPT : __ptr_(__p) {}
    _LIBCPP_INLINE_VISIBILITY
    __node_pointer __get_np() const { return static_cast<__node_pointer>(__ptr_); }
    template <class, class, class> friend class __tree;
    template <class, class, class> friend class _LIBCPP_TEMPLATE_VIS __tree_const_iterator;
    template <class> friend class _LIBCPP_TEMPLATE_VIS __map_iterator;
    template <class, class, class, class> friend class _LIBCPP_TEMPLATE_VIS map;
    template <class, class, class, class> friend class _LIBCPP_TEMPLATE_VIS multimap;
    template <class, class, class> friend class _LIBCPP_TEMPLATE_VIS set;
    template <class, class, class> friend class _LIBCPP_TEMPLATE_VIS multiset;
};

template <class _Tp, class _NodePtr, class _DiffType>
class _LIBCPP_TEMPLATE_VIS __tree_const_iterator
{
    typedef __tree_node_types<_NodePtr>                     _NodeTypes;
    typedef typename _NodeTypes::__node_pointer             __node_pointer;
    typedef typename _NodeTypes::__node_base_pointer        __node_base_pointer;
    typedef typename _NodeTypes::__end_node_pointer         __end_node_pointer;
    typedef typename _NodeTypes::__iter_pointer             __iter_pointer;
    typedef pointer_traits<__node_pointer> __pointer_traits;

    __iter_pointer __ptr_;

public:
    typedef bidirectional_iterator_tag                           iterator_category;
    typedef _Tp                                                  value_type;
    typedef _DiffType                                            difference_type;
    typedef const value_type&                                    reference;
    typedef typename _NodeTypes::__const_node_value_type_pointer pointer;

    _LIBCPP_INLINE_VISIBILITY __tree_const_iterator() _NOEXCEPT
#if _LIBCPP_STD_VER > 11
    : __ptr_(nullptr)
#endif
    {}

private:
    typedef __tree_iterator<value_type, __node_pointer, difference_type>
                                                           __non_const_iterator;
public:
    _LIBCPP_INLINE_VISIBILITY
    __tree_const_iterator(__non_const_iterator __p) _NOEXCEPT
        : __ptr_(__p.__ptr_) {}

    _LIBCPP_INLINE_VISIBILITY reference operator*() const
        {return __get_np()->__value_;}
    _LIBCPP_INLINE_VISIBILITY pointer operator->() const
        {return pointer_traits<pointer>::pointer_to(__get_np()->__value_);}

    _LIBCPP_INLINE_VISIBILITY
    __tree_const_iterator& operator++() {
      __ptr_ = static_cast<__iter_pointer>(
          __tree_next_iter<__end_node_pointer>(static_cast<__node_base_pointer>(__ptr_)));
      return *this;
    }

    _LIBCPP_INLINE_VISIBILITY
    __tree_const_iterator operator++(int)
        {__tree_const_iterator __t(*this); ++(*this); return __t;}

    _LIBCPP_INLINE_VISIBILITY
    __tree_const_iterator& operator--() {
      __ptr_ = static_cast<__iter_pointer>(__tree_prev_iter<__node_base_pointer>(
          static_cast<__end_node_pointer>(__ptr_)));
      return *this;
    }

    _LIBCPP_INLINE_VISIBILITY
    __tree_const_iterator operator--(int)
        {__tree_const_iterator __t(*this); --(*this); return __t;}

    friend _LIBCPP_INLINE_VISIBILITY
        bool operator==(const __tree_const_iterator& __x, const __tree_const_iterator& __y)
        {return __x.__ptr_ == __y.__ptr_;}
    friend _LIBCPP_INLINE_VISIBILITY
        bool operator!=(const __tree_const_iterator& __x, const __tree_const_iterator& __y)
        {return !(__x == __y);}

private:
    _LIBCPP_INLINE_VISIBILITY
    explicit __tree_const_iterator(__node_pointer __p) _NOEXCEPT
        : __ptr_(__p) {}
    _LIBCPP_INLINE_VISIBILITY
    explicit __tree_const_iterator(__end_node_pointer __p) _NOEXCEPT
        : __ptr_(__p) {}
    _LIBCPP_INLINE_VISIBILITY
    __node_pointer __get_np() const { return static_cast<__node_pointer>(__ptr_); }

    template <class, class, class> friend class __tree;
    template <class, class, class, class> friend class _LIBCPP_TEMPLATE_VIS map;
    template <class, class, class, class> friend class _LIBCPP_TEMPLATE_VIS multimap;
    template <class, class, class> friend class _LIBCPP_TEMPLATE_VIS set;
    template <class, class, class> friend class _LIBCPP_TEMPLATE_VIS multiset;
    template <class> friend class _LIBCPP_TEMPLATE_VIS __map_const_iterator;

};

template<class _Tp, class _Compare>
#ifndef _LIBCPP_CXX03_LANG
    _LIBCPP_DIAGNOSE_WARNING(!std::__invokable<_Compare const&, _Tp const&, _Tp const&>::value,
        "the specified comparator type does not provide a viable const call operator")
#endif
int __diagnose_non_const_comparator();

template <class _Tp, class _Compare, class _Allocator>
class __tree
{
public:
    typedef _Tp                                      value_type;
    typedef _Compare                                 value_compare;
    typedef _Allocator                               allocator_type;

private:
    typedef allocator_traits<allocator_type>         __alloc_traits;
    typedef typename __make_tree_node_types<value_type,
        typename __alloc_traits::void_pointer>::type
                                                    _NodeTypes;
    typedef typename _NodeTypes::key_type           key_type;
public:
    typedef typename _NodeTypes::__node_value_type      __node_value_type;
    typedef typename _NodeTypes::__container_value_type __container_value_type;

    typedef typename __alloc_traits::pointer         pointer;
    typedef typename __alloc_traits::const_pointer   const_pointer;
    typedef typename __alloc_traits::size_type       size_type;
    typedef typename __alloc_traits::difference_type difference_type;

public:
    typedef typename _NodeTypes::__void_pointer        __void_pointer;

    typedef typename _NodeTypes::__node_type           __node;
    typedef typename _NodeTypes::__node_pointer        __node_pointer;

    typedef typename _NodeTypes::__node_base_type      __node_base;
    typedef typename _NodeTypes::__node_base_pointer   __node_base_pointer;

    typedef typename _NodeTypes::__end_node_type       __end_node_t;
    typedef typename _NodeTypes::__end_node_pointer    __end_node_ptr;

    typedef typename _NodeTypes::__parent_pointer      __parent_pointer;
    typedef typename _NodeTypes::__iter_pointer        __iter_pointer;

    typedef typename __rebind_alloc_helper<__alloc_traits, __node>::type __node_allocator;
    typedef allocator_traits<__node_allocator>         __node_traits;

private:
    // check for sane allocator pointer rebinding semantics. Rebinding the
    // allocator for a new pointer type should be exactly the same as rebinding
    // the pointer using 'pointer_traits'.
    static_assert((is_same<__node_pointer, typename __node_traits::pointer>::value),
                  "Allocator does not rebind pointers in a sane manner.");
    typedef typename __rebind_alloc_helper<__node_traits, __node_base>::type
        __node_base_allocator;
    typedef allocator_traits<__node_base_allocator> __node_base_traits;
    static_assert((is_same<__node_base_pointer, typename __node_base_traits::pointer>::value),
                 "Allocator does not rebind pointers in a sane manner.");

private:
    __iter_pointer                                     __begin_node_;
    __compressed_pair<__end_node_t, __node_allocator>  __pair1_;
    __compressed_pair<size_type, value_compare>        __pair3_;

public:
    _LIBCPP_INLINE_VISIBILITY
    __iter_pointer __end_node() _NOEXCEPT
    {
        return static_cast<__iter_pointer>(
                pointer_traits<__end_node_ptr>::pointer_to(__pair1_.first())
        );
    }
    _LIBCPP_INLINE_VISIBILITY
    __iter_pointer __end_node() const _NOEXCEPT
    {
        return static_cast<__iter_pointer>(
            pointer_traits<__end_node_ptr>::pointer_to(
                const_cast<__end_node_t&>(__pair1_.first())
            )
        );
    }
    _LIBCPP_INLINE_VISIBILITY
          __node_allocator& __node_alloc() _NOEXCEPT {return __pair1_.second();}
private:
    _LIBCPP_INLINE_VISIBILITY
    const __node_allocator& __node_alloc() const _NOEXCEPT
        {return __pair1_.second();}
    _LIBCPP_INLINE_VISIBILITY
          __iter_pointer& __begin_node() _NOEXCEPT {return __begin_node_;}
    _LIBCPP_INLINE_VISIBILITY
    const __iter_pointer& __begin_node() const _NOEXCEPT {return __begin_node_;}
public:
    _LIBCPP_INLINE_VISIBILITY
    allocator_type __alloc() const _NOEXCEPT
        {return allocator_type(__node_alloc());}
private:
    _LIBCPP_INLINE_VISIBILITY
          size_type& size() _NOEXCEPT {return __pair3_.first();}
public:
    _LIBCPP_INLINE_VISIBILITY
    const size_type& size() const _NOEXCEPT {return __pair3_.first();}
    _LIBCPP_INLINE_VISIBILITY
          value_compare& value_comp() _NOEXCEPT {return __pair3_.second();}
    _LIBCPP_INLINE_VISIBILITY
    const value_compare& value_comp() const _NOEXCEPT
        {return __pair3_.second();}
public:

    _LIBCPP_INLINE_VISIBILITY
    __node_pointer __root() const _NOEXCEPT
        {return static_cast<__node_pointer>(__end_node()->__left_);}

    __node_base_pointer* __root_ptr() const _NOEXCEPT {
        return _VSTD::addressof(__end_node()->__left_);
    }

    typedef __tree_iterator<value_type, __node_pointer, difference_type>             iterator;
    typedef __tree_const_iterator<value_type, __node_pointer, difference_type> const_iterator;

    explicit __tree(const value_compare& __comp)
        _NOEXCEPT_(
            is_nothrow_default_constructible<__node_allocator>::value &&
            is_nothrow_copy_constructible<value_compare>::value);
    explicit __tree(const allocator_type& __a);
    __tree(const value_compare& __comp, const allocator_type& __a);
    __tree(const __tree& __t);
    __tree& operator=(const __tree& __t);
    template <class _ForwardIterator>
        void __assign_unique(_ForwardIterator __first, _ForwardIterator __last);
    template <class _InputIterator>
        void __assign_multi(_InputIterator __first, _InputIterator __last);
#ifndef _LIBCPP_CXX03_LANG
    __tree(__tree&& __t)
        _NOEXCEPT_(
            is_nothrow_move_constructible<__node_allocator>::value &&
            is_nothrow_move_constructible<value_compare>::value);
    __tree(__tree&& __t, const allocator_type& __a);
    __tree& operator=(__tree&& __t)
        _NOEXCEPT_(
            __node_traits::propagate_on_container_move_assignment::value &&
            is_nothrow_move_assignable<value_compare>::value &&
            is_nothrow_move_assignable<__node_allocator>::value);
#endif // _LIBCPP_CXX03_LANG

    ~__tree();

    _LIBCPP_INLINE_VISIBILITY
          iterator begin()  _NOEXCEPT {return       iterator(__begin_node());}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator begin() const _NOEXCEPT {return const_iterator(__begin_node());}
    _LIBCPP_INLINE_VISIBILITY
          iterator end() _NOEXCEPT {return       iterator(__end_node());}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator end() const _NOEXCEPT {return const_iterator(__end_node());}

    _LIBCPP_INLINE_VISIBILITY
    size_type max_size() const _NOEXCEPT
        {return std::min<size_type>(
                __node_traits::max_size(__node_alloc()),
                numeric_limits<difference_type >::max());}

    void clear() _NOEXCEPT;

    void swap(__tree& __t)
#if _LIBCPP_STD_VER <= 11
        _NOEXCEPT_(
            __is_nothrow_swappable<value_compare>::value
            && (!__node_traits::propagate_on_container_swap::value ||
                 __is_nothrow_swappable<__node_allocator>::value)
            );
#else
        _NOEXCEPT_(__is_nothrow_swappable<value_compare>::value);
#endif

#ifndef _LIBCPP_CXX03_LANG
    template <class _Key, class ..._Args>
    pair<iterator, bool>
    __emplace_unique_key_args(_Key const&, _Args&&... __args);
    template <class _Key, class ..._Args>
    iterator
    __emplace_hint_unique_key_args(const_iterator, _Key const&, _Args&&...);

    template <class... _Args>
    pair<iterator, bool> __emplace_unique_impl(_Args&&... __args);

    template <class... _Args>
    iterator __emplace_hint_unique_impl(const_iterator __p, _Args&&... __args);

    template <class... _Args>
    iterator __emplace_multi(_Args&&... __args);

    template <class... _Args>
    iterator __emplace_hint_multi(const_iterator __p, _Args&&... __args);

    template <class _Pp>
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool> __emplace_unique(_Pp&& __x) {
        return __emplace_unique_extract_key(_VSTD::forward<_Pp>(__x),
                                            __can_extract_key<_Pp, key_type>());
    }

    template <class _First, class _Second>
    _LIBCPP_INLINE_VISIBILITY
    typename enable_if<
        __can_extract_map_key<_First, key_type, __container_value_type>::value,
        pair<iterator, bool>
    >::type __emplace_unique(_First&& __f, _Second&& __s) {
        return __emplace_unique_key_args(__f, _VSTD::forward<_First>(__f),
                                              _VSTD::forward<_Second>(__s));
    }

    template <class... _Args>
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool> __emplace_unique(_Args&&... __args) {
        return __emplace_unique_impl(_VSTD::forward<_Args>(__args)...);
    }

    template <class _Pp>
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool>
    __emplace_unique_extract_key(_Pp&& __x, __extract_key_fail_tag) {
      return __emplace_unique_impl(_VSTD::forward<_Pp>(__x));
    }

    template <class _Pp>
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool>
    __emplace_unique_extract_key(_Pp&& __x, __extract_key_self_tag) {
      return __emplace_unique_key_args(__x, _VSTD::forward<_Pp>(__x));
    }

    template <class _Pp>
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool>
    __emplace_unique_extract_key(_Pp&& __x, __extract_key_first_tag) {
      return __emplace_unique_key_args(__x.first, _VSTD::forward<_Pp>(__x));
    }

    template <class _Pp>
    _LIBCPP_INLINE_VISIBILITY
    iterator __emplace_hint_unique(const_iterator __p, _Pp&& __x) {
        return __emplace_hint_unique_extract_key(__p, _VSTD::forward<_Pp>(__x),
                                            __can_extract_key<_Pp, key_type>());
    }

    template <class _First, class _Second>
    _LIBCPP_INLINE_VISIBILITY
    typename enable_if<
        __can_extract_map_key<_First, key_type, __container_value_type>::value,
        iterator
    >::type __emplace_hint_unique(const_iterator __p, _First&& __f, _Second&& __s) {
        return __emplace_hint_unique_key_args(__p, __f,
                                              _VSTD::forward<_First>(__f),
                                              _VSTD::forward<_Second>(__s));
    }

    template <class... _Args>
    _LIBCPP_INLINE_VISIBILITY
    iterator __emplace_hint_unique(const_iterator __p, _Args&&... __args) {
        return __emplace_hint_unique_impl(__p, _VSTD::forward<_Args>(__args)...);
    }

    template <class _Pp>
    _LIBCPP_INLINE_VISIBILITY
    iterator
    __emplace_hint_unique_extract_key(const_iterator __p, _Pp&& __x, __extract_key_fail_tag) {
      return __emplace_hint_unique_impl(__p, _VSTD::forward<_Pp>(__x));
    }

    template <class _Pp>
    _LIBCPP_INLINE_VISIBILITY
    iterator
    __emplace_hint_unique_extract_key(const_iterator __p, _Pp&& __x, __extract_key_self_tag) {
      return __emplace_hint_unique_key_args(__p, __x, _VSTD::forward<_Pp>(__x));
    }

    template <class _Pp>
    _LIBCPP_INLINE_VISIBILITY
    iterator
    __emplace_hint_unique_extract_key(const_iterator __p, _Pp&& __x, __extract_key_first_tag) {
      return __emplace_hint_unique_key_args(__p, __x.first, _VSTD::forward<_Pp>(__x));
    }

#else
    template <class _Key, class _Args>
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool> __emplace_unique_key_args(_Key const&, _Args& __args);
    template <class _Key, class _Args>
    _LIBCPP_INLINE_VISIBILITY
    iterator __emplace_hint_unique_key_args(const_iterator, _Key const&, _Args&);
#endif

    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool> __insert_unique(const __container_value_type& __v) {
        return __emplace_unique_key_args(_NodeTypes::__get_key(__v), __v);
    }

    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_unique(const_iterator __p, const __container_value_type& __v) {
        return __emplace_hint_unique_key_args(__p, _NodeTypes::__get_key(__v), __v);
    }

#ifdef _LIBCPP_CXX03_LANG
    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_multi(const __container_value_type& __v);
    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_multi(const_iterator __p, const __container_value_type& __v);
#else
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool> __insert_unique(__container_value_type&& __v) {
        return __emplace_unique_key_args(_NodeTypes::__get_key(__v), _VSTD::move(__v));
    }

    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_unique(const_iterator __p, __container_value_type&& __v) {
        return __emplace_hint_unique_key_args(__p, _NodeTypes::__get_key(__v), _VSTD::move(__v));
    }

    template <class _Vp, class = typename enable_if<
            !is_same<typename __unconstref<_Vp>::type,
                     __container_value_type
            >::value
        >::type>
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool> __insert_unique(_Vp&& __v) {
        return __emplace_unique(_VSTD::forward<_Vp>(__v));
    }

    template <class _Vp, class = typename enable_if<
            !is_same<typename __unconstref<_Vp>::type,
                     __container_value_type
            >::value
        >::type>
    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_unique(const_iterator __p, _Vp&& __v) {
        return __emplace_hint_unique(__p, _VSTD::forward<_Vp>(__v));
    }

    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_multi(__container_value_type&& __v) {
        return __emplace_multi(_VSTD::move(__v));
    }

    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_multi(const_iterator __p, __container_value_type&& __v) {
        return __emplace_hint_multi(__p, _VSTD::move(__v));
    }

    template <class _Vp>
    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_multi(_Vp&& __v) {
        return __emplace_multi(_VSTD::forward<_Vp>(__v));
    }

    template <class _Vp>
    _LIBCPP_INLINE_VISIBILITY
    iterator __insert_multi(const_iterator __p, _Vp&& __v) {
        return __emplace_hint_multi(__p, _VSTD::forward<_Vp>(__v));
    }

#endif // !_LIBCPP_CXX03_LANG

    _LIBCPP_INLINE_VISIBILITY
    pair<iterator, bool> __node_assign_unique(const __container_value_type& __v, __node_pointer __dest);

    _LIBCPP_INLINE_VISIBILITY
    iterator __node_insert_multi(__node_pointer __nd);
    _LIBCPP_INLINE_VISIBILITY
    iterator __node_insert_multi(const_iterator __p, __node_pointer __nd);


    _LIBCPP_INLINE_VISIBILITY iterator
    __remove_node_pointer(__node_pointer) _NOEXCEPT;

#if _LIBCPP_STD_VER > 14
    template <class _NodeHandle, class _InsertReturnType>
    _LIBCPP_INLINE_VISIBILITY
    _InsertReturnType __node_handle_insert_unique(_NodeHandle&&);
    template <class _NodeHandle>
    _LIBCPP_INLINE_VISIBILITY
    iterator __node_handle_insert_unique(const_iterator, _NodeHandle&&);
    template <class _Tree>
    _LIBCPP_INLINE_VISIBILITY
    void __node_handle_merge_unique(_Tree& __source);

    template <class _NodeHandle>
    _LIBCPP_INLINE_VISIBILITY
    iterator __node_handle_insert_multi(_NodeHandle&&);
    template <class _NodeHandle>
    _LIBCPP_INLINE_VISIBILITY
    iterator __node_handle_insert_multi(const_iterator, _NodeHandle&&);
    template <class _Tree>
    _LIBCPP_INLINE_VISIBILITY
    void __node_handle_merge_multi(_Tree& __source);


    template <class _NodeHandle>
    _LIBCPP_INLINE_VISIBILITY
    _NodeHandle __node_handle_extract(key_type const&);
    template <class _NodeHandle>
    _LIBCPP_INLINE_VISIBILITY
    _NodeHandle __node_handle_extract(const_iterator);
#endif

    iterator erase(const_iterator __p);
    iterator erase(const_iterator __f, const_iterator __l);
    template <class _Key>
        size_type __erase_unique(const _Key& __k);
    template <class _Key>
        size_type __erase_multi(const _Key& __k);

    void __insert_node_at(__parent_pointer     __parent,
                          __node_base_pointer& __child,
                          __node_base_pointer __new_node) _NOEXCEPT;

    template <class _Key>
        iterator find(const _Key& __v);
    template <class _Key>
        const_iterator find(const _Key& __v) const;

    template <class _Key>
        size_type __count_unique(const _Key& __k) const;
    template <class _Key>
        size_type __count_multi(const _Key& __k) const;

    template <class _Key>
        _LIBCPP_INLINE_VISIBILITY
        iterator lower_bound(const _Key& __v)
            {return __lower_bound(__v, __root(), __end_node());}
    template <class _Key>
        iterator __lower_bound(const _Key& __v,
                               __node_pointer __root,
                               __iter_pointer __result);
    template <class _Key>
        _LIBCPP_INLINE_VISIBILITY
        const_iterator lower_bound(const _Key& __v) const
            {return __lower_bound(__v, __root(), __end_node());}
    template <class _Key>
        const_iterator __lower_bound(const _Key& __v,
                                     __node_pointer __root,
                                     __iter_pointer __result) const;
    template <class _Key>
        _LIBCPP_INLINE_VISIBILITY
        iterator upper_bound(const _Key& __v)
            {return __upper_bound(__v, __root(), __end_node());}
    template <class _Key>
        iterator __upper_bound(const _Key& __v,
                               __node_pointer __root,
                               __iter_pointer __result);
    template <class _Key>
        _LIBCPP_INLINE_VISIBILITY
        const_iterator upper_bound(const _Key& __v) const
            {return __upper_bound(__v, __root(), __end_node());}
    template <class _Key>
        const_iterator __upper_bound(const _Key& __v,
                                     __node_pointer __root,
                                     __iter_pointer __result) const;
    template <class _Key>
        pair<iterator, iterator>
        __equal_range_unique(const _Key& __k);
    template <class _Key>
        pair<const_iterator, const_iterator>
        __equal_range_unique(const _Key& __k) const;

    template <class _Key>
        pair<iterator, iterator>
        __equal_range_multi(const _Key& __k);
    template <class _Key>
        pair<const_iterator, const_iterator>
        __equal_range_multi(const _Key& __k) const;

    typedef __tree_node_destructor<__node_allocator> _Dp;
    typedef unique_ptr<__node, _Dp> __node_holder;

    __node_holder remove(const_iterator __p) _NOEXCEPT;
private:
    __node_base_pointer&
        __find_leaf_low(__parent_pointer& __parent, const key_type& __v);
    __node_base_pointer&
        __find_leaf_high(__parent_pointer& __parent, const key_type& __v);
    __node_base_pointer&
        __find_leaf(const_iterator __hint,
                    __parent_pointer& __parent, const key_type& __v);
    // FIXME: Make this function const qualified. Unfortunetly doing so
    // breaks existing code which uses non-const callable comparators.
    template <class _Key>
    __node_base_pointer&
        __find_equal(__parent_pointer& __parent, const _Key& __v);
    template <class _Key>
    _LIBCPP_INLINE_VISIBILITY __node_base_pointer&
    __find_equal(__parent_pointer& __parent, const _Key& __v) const {
      return const_cast<__tree*>(this)->__find_equal(__parent, __v);
    }
    template <class _Key>
    __node_base_pointer&
        __find_equal(const_iterator __hint, __parent_pointer& __parent,
                     __node_base_pointer& __dummy,
                     const _Key& __v);

#ifndef _LIBCPP_CXX03_LANG
    template <class ..._Args>
    __node_holder __construct_node(_Args&& ...__args);
#else
    __node_holder __construct_node(const __container_value_type& __v);
#endif

    void destroy(__node_pointer __nd) _NOEXCEPT;

    _LIBCPP_INLINE_VISIBILITY
    void __copy_assign_alloc(const __tree& __t)
        {__copy_assign_alloc(__t, integral_constant<bool,
             __node_traits::propagate_on_container_copy_assignment::value>());}

    _LIBCPP_INLINE_VISIBILITY
    void __copy_assign_alloc(const __tree& __t, true_type)
        {
        if (__node_alloc() != __t.__node_alloc())
            clear();
        __node_alloc() = __t.__node_alloc();
        }
    _LIBCPP_INLINE_VISIBILITY
    void __copy_assign_alloc(const __tree&, false_type) {}

    void __move_assign(__tree& __t, false_type);
    void __move_assign(__tree& __t, true_type)
        _NOEXCEPT_(is_nothrow_move_assignable<value_compare>::value &&
                   is_nothrow_move_assignable<__node_allocator>::value);

    _LIBCPP_INLINE_VISIBILITY
    void __move_assign_alloc(__tree& __t)
        _NOEXCEPT_(
            !__node_traits::propagate_on_container_move_assignment::value ||
            is_nothrow_move_assignable<__node_allocator>::value)
        {__move_assign_alloc(__t, integral_constant<bool,
             __node_traits::propagate_on_container_move_assignment::value>());}

    _LIBCPP_INLINE_VISIBILITY
    void __move_assign_alloc(__tree& __t, true_type)
        _NOEXCEPT_(is_nothrow_move_assignable<__node_allocator>::value)
        {__node_alloc() = _VSTD::move(__t.__node_alloc());}
    _LIBCPP_INLINE_VISIBILITY
    void __move_assign_alloc(__tree&, false_type) _NOEXCEPT {}

    struct _DetachedTreeCache {
      _LIBCPP_INLINE_VISIBILITY
      explicit _DetachedTreeCache(__tree *__t) _NOEXCEPT : __t_(__t),
        __cache_root_(__detach_from_tree(__t)) {
          __advance();
        }

      _LIBCPP_INLINE_VISIBILITY
      __node_pointer __get() const _NOEXCEPT {
        return __cache_elem_;
      }

      _LIBCPP_INLINE_VISIBILITY
      void __advance() _NOEXCEPT {
        __cache_elem_ = __cache_root_;
        if (__cache_root_) {
          __cache_root_ = __detach_next(__cache_root_);
        }
      }

      _LIBCPP_INLINE_VISIBILITY
      ~_DetachedTreeCache() {
        __t_->destroy(__cache_elem_);
        if (__cache_root_) {
          while (__cache_root_->__parent_ != nullptr)
            __cache_root_ = static_cast<__node_pointer>(__cache_root_->__parent_);
          __t_->destroy(__cache_root_);
        }
      }

       _DetachedTreeCache(_DetachedTreeCache const&) = delete;
       _DetachedTreeCache& operator=(_DetachedTreeCache const&) = delete;

    private:
      _LIBCPP_INLINE_VISIBILITY
      static __node_pointer __detach_from_tree(__tree *__t) _NOEXCEPT;
      _LIBCPP_INLINE_VISIBILITY
      static __node_pointer __detach_next(__node_pointer) _NOEXCEPT;

      __tree *__t_;
      __node_pointer __cache_root_;
      __node_pointer __cache_elem_;
    };


    template <class, class, class, class> friend class _LIBCPP_TEMPLATE_VIS map;
    template <class, class, class, class> friend class _LIBCPP_TEMPLATE_VIS multimap;
};

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const value_compare& __comp)
        _NOEXCEPT_(
            is_nothrow_default_constructible<__node_allocator>::value &&
            is_nothrow_copy_constructible<value_compare>::value)
    : __pair3_(0, __comp)
{
    __begin_node() = __end_node();
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const allocator_type& __a)
    : __begin_node_(__iter_pointer()),
      __pair1_(__default_init_tag(), __node_allocator(__a)),
      __pair3_(0, __default_init_tag())
{
    __begin_node() = __end_node();
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const value_compare& __comp,
                                           const allocator_type& __a)
    : __begin_node_(__iter_pointer()),
      __pair1_(__default_init_tag(), __node_allocator(__a)),
      __pair3_(0, __comp)
{
    __begin_node() = __end_node();
}

// Precondition:  size() != 0
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_pointer
__tree<_Tp, _Compare, _Allocator>::_DetachedTreeCache::__detach_from_tree(__tree *__t) _NOEXCEPT
{
    __node_pointer __cache = static_cast<__node_pointer>(__t->__begin_node());
    __t->__begin_node() = __t->__end_node();
    __t->__end_node()->__left_->__parent_ = nullptr;
    __t->__end_node()->__left_ = nullptr;
    __t->size() = 0;
    // __cache->__left_ == nullptr
    if (__cache->__right_ != nullptr)
        __cache = static_cast<__node_pointer>(__cache->__right_);
    // __cache->__left_ == nullptr
    // __cache->__right_ == nullptr
    return __cache;
}

// Precondition:  __cache != nullptr
//    __cache->left_ == nullptr
//    __cache->right_ == nullptr
//    This is no longer a red-black tree
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_pointer
__tree<_Tp, _Compare, _Allocator>::_DetachedTreeCache::__detach_next(__node_pointer __cache) _NOEXCEPT
{
    if (__cache->__parent_ == nullptr)
        return nullptr;
    if (__tree_is_left_child(static_cast<__node_base_pointer>(__cache)))
    {
        __cache->__parent_->__left_ = nullptr;
        __cache = static_cast<__node_pointer>(__cache->__parent_);
        if (__cache->__right_ == nullptr)
            return __cache;
        return static_cast<__node_pointer>(__tree_leaf(__cache->__right_));
    }
    // __cache is right child
    __cache->__parent_unsafe()->__right_ = nullptr;
    __cache = static_cast<__node_pointer>(__cache->__parent_);
    if (__cache->__left_ == nullptr)
        return __cache;
    return static_cast<__node_pointer>(__tree_leaf(__cache->__left_));
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>&
__tree<_Tp, _Compare, _Allocator>::operator=(const __tree& __t)
{
    if (this != &__t)
    {
        value_comp() = __t.value_comp();
        __copy_assign_alloc(__t);
        __assign_multi(__t.begin(), __t.end());
    }
    return *this;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _ForwardIterator>
void
__tree<_Tp, _Compare, _Allocator>::__assign_unique(_ForwardIterator __first, _ForwardIterator __last)
{
    typedef iterator_traits<_ForwardIterator> _ITraits;
    typedef typename _ITraits::value_type _ItValueType;
    static_assert((is_same<_ItValueType, __container_value_type>::value),
                  "__assign_unique may only be called with the containers value type");
    static_assert(__is_cpp17_forward_iterator<_ForwardIterator>::value,
                  "__assign_unique requires a forward iterator");
    if (size() != 0)
    {
        _DetachedTreeCache __cache(this);
          for (; __cache.__get() != nullptr && __first != __last; ++__first) {
              if (__node_assign_unique(*__first, __cache.__get()).second)
                  __cache.__advance();
            }
    }
    for (; __first != __last; ++__first)
        __insert_unique(*__first);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _InputIterator>
void
__tree<_Tp, _Compare, _Allocator>::__assign_multi(_InputIterator __first, _InputIterator __last)
{
    typedef iterator_traits<_InputIterator> _ITraits;
    typedef typename _ITraits::value_type _ItValueType;
    static_assert((is_same<_ItValueType, __container_value_type>::value ||
                  is_same<_ItValueType, __node_value_type>::value),
                  "__assign_multi may only be called with the containers value type"
                  " or the nodes value type");
    if (size() != 0)
    {
        _DetachedTreeCache __cache(this);
        for (; __cache.__get() && __first != __last; ++__first) {
            __cache.__get()->__value_ = *__first;
            __node_insert_multi(__cache.__get());
            __cache.__advance();
        }
    }
    for (; __first != __last; ++__first)
        __insert_multi(_NodeTypes::__get_value(*__first));
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const __tree& __t)
    : __begin_node_(__iter_pointer()),
      __pair1_(__default_init_tag(), __node_traits::select_on_container_copy_construction(__t.__node_alloc())),
      __pair3_(0, __t.value_comp())
{
    __begin_node() = __end_node();
}

#ifndef _LIBCPP_CXX03_LANG

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(__tree&& __t)
    _NOEXCEPT_(
        is_nothrow_move_constructible<__node_allocator>::value &&
        is_nothrow_move_constructible<value_compare>::value)
    : __begin_node_(_VSTD::move(__t.__begin_node_)),
      __pair1_(_VSTD::move(__t.__pair1_)),
      __pair3_(_VSTD::move(__t.__pair3_))
{
    if (size() == 0)
        __begin_node() = __end_node();
    else
    {
        __end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__end_node());
        __t.__begin_node() = __t.__end_node();
        __t.__end_node()->__left_ = nullptr;
        __t.size() = 0;
    }
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(__tree&& __t, const allocator_type& __a)
    : __pair1_(__default_init_tag(), __node_allocator(__a)),
      __pair3_(0, _VSTD::move(__t.value_comp()))
{
    if (__a == __t.__alloc())
    {
        if (__t.size() == 0)
            __begin_node() = __end_node();
        else
        {
            __begin_node() = __t.__begin_node();
            __end_node()->__left_ = __t.__end_node()->__left_;
            __end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__end_node());
            size() = __t.size();
            __t.__begin_node() = __t.__end_node();
            __t.__end_node()->__left_ = nullptr;
            __t.size() = 0;
        }
    }
    else
    {
        __begin_node() = __end_node();
    }
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::__move_assign(__tree& __t, true_type)
    _NOEXCEPT_(is_nothrow_move_assignable<value_compare>::value &&
               is_nothrow_move_assignable<__node_allocator>::value)
{
    destroy(static_cast<__node_pointer>(__end_node()->__left_));
    __begin_node_ = __t.__begin_node_;
    __pair1_.first() = __t.__pair1_.first();
    __move_assign_alloc(__t);
    __pair3_ = _VSTD::move(__t.__pair3_);
    if (size() == 0)
        __begin_node() = __end_node();
    else
    {
        __end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__end_node());
        __t.__begin_node() = __t.__end_node();
        __t.__end_node()->__left_ = nullptr;
        __t.size() = 0;
    }
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::__move_assign(__tree& __t, false_type)
{
    if (__node_alloc() == __t.__node_alloc())
        __move_assign(__t, true_type());
    else
    {
        value_comp() = _VSTD::move(__t.value_comp());
        const_iterator __e = end();
        if (size() != 0)
        {
            _DetachedTreeCache __cache(this);
            while (__cache.__get() != nullptr && __t.size() != 0) {
              __cache.__get()->__value_ = _VSTD::move(__t.remove(__t.begin())->__value_);
              __node_insert_multi(__cache.__get());
              __cache.__advance();
            }
        }
        while (__t.size() != 0)
            __insert_multi(__e, _NodeTypes::__move(__t.remove(__t.begin())->__value_));
    }
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>&
__tree<_Tp, _Compare, _Allocator>::operator=(__tree&& __t)
    _NOEXCEPT_(
        __node_traits::propagate_on_container_move_assignment::value &&
        is_nothrow_move_assignable<value_compare>::value &&
        is_nothrow_move_assignable<__node_allocator>::value)

{
    __move_assign(__t, integral_constant<bool,
                  __node_traits::propagate_on_container_move_assignment::value>());
    return *this;
}

#endif  // _LIBCPP_CXX03_LANG

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::~__tree()
{
    static_assert((is_copy_constructible<value_compare>::value),
                 "Comparator must be copy-constructible.");
  destroy(__root());
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::destroy(__node_pointer __nd) _NOEXCEPT
{
    if (__nd != nullptr)
    {
        destroy(static_cast<__node_pointer>(__nd->__left_));
        destroy(static_cast<__node_pointer>(__nd->__right_));
        __node_allocator& __na = __node_alloc();
        __node_traits::destroy(__na, _NodeTypes::__get_ptr(__nd->__value_));
        __node_traits::deallocate(__na, __nd, 1);
    }
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::swap(__tree& __t)
#if _LIBCPP_STD_VER <= 11
        _NOEXCEPT_(
            __is_nothrow_swappable<value_compare>::value
            && (!__node_traits::propagate_on_container_swap::value ||
                 __is_nothrow_swappable<__node_allocator>::value)
            )
#else
        _NOEXCEPT_(__is_nothrow_swappable<value_compare>::value)
#endif
{
    using _VSTD::swap;
    swap(__begin_node_, __t.__begin_node_);
    swap(__pair1_.first(), __t.__pair1_.first());
    __swap_allocator(__node_alloc(), __t.__node_alloc());
    __pair3_.swap(__t.__pair3_);
    if (size() == 0)
        __begin_node() = __end_node();
    else
        __end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__end_node());
    if (__t.size() == 0)
        __t.__begin_node() = __t.__end_node();
    else
        __t.__end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__t.__end_node());
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::clear() _NOEXCEPT
{
    destroy(__root());
    size() = 0;
    __begin_node() = __end_node();
    __end_node()->__left_ = nullptr;
}

// Find lower_bound place to insert
// Set __parent to parent of null leaf
// Return reference to null leaf
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_leaf_low(__parent_pointer& __parent,
                                                   const key_type& __v)
{
    __node_pointer __nd = __root();
    if (__nd != nullptr)
    {
        while (true)
        {
            if (value_comp()(__nd->__value_, __v))
            {
                if (__nd->__right_ != nullptr)
                    __nd = static_cast<__node_pointer>(__nd->__right_);
                else
                {
                    __parent = static_cast<__parent_pointer>(__nd);
                    return __nd->__right_;
                }
            }
            else
            {
                if (__nd->__left_ != nullptr)
                    __nd = static_cast<__node_pointer>(__nd->__left_);
                else
                {
                    __parent = static_cast<__parent_pointer>(__nd);
                    return __parent->__left_;
                }
            }
        }
    }
    __parent = static_cast<__parent_pointer>(__end_node());
    return __parent->__left_;
}

// Find upper_bound place to insert
// Set __parent to parent of null leaf
// Return reference to null leaf
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_leaf_high(__parent_pointer& __parent,
                                                    const key_type& __v)
{
    __node_pointer __nd = __root();
    if (__nd != nullptr)
    {
        while (true)
        {
            if (value_comp()(__v, __nd->__value_))
            {
                if (__nd->__left_ != nullptr)
                    __nd = static_cast<__node_pointer>(__nd->__left_);
                else
                {
                    __parent = static_cast<__parent_pointer>(__nd);
                    return __parent->__left_;
                }
            }
            else
            {
                if (__nd->__right_ != nullptr)
                    __nd = static_cast<__node_pointer>(__nd->__right_);
                else
                {
                    __parent = static_cast<__parent_pointer>(__nd);
                    return __nd->__right_;
                }
            }
        }
    }
    __parent = static_cast<__parent_pointer>(__end_node());
    return __parent->__left_;
}

// Find leaf place to insert closest to __hint
// First check prior to __hint.
// Next check after __hint.
// Next do O(log N) search.
// Set __parent to parent of null leaf
// Return reference to null leaf
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_leaf(const_iterator __hint,
                                               __parent_pointer& __parent,
                                               const key_type& __v)
{
    if (__hint == end() || !value_comp()(*__hint, __v))  // check before
    {
        // __v <= *__hint
        const_iterator __prior = __hint;
        if (__prior == begin() || !value_comp()(__v, *--__prior))
        {
            // *prev(__hint) <= __v <= *__hint
            if (__hint.__ptr_->__left_ == nullptr)
            {
                __parent = static_cast<__parent_pointer>(__hint.__ptr_);
                return __parent->__left_;
            }
            else
            {
                __parent = static_cast<__parent_pointer>(__prior.__ptr_);
                return static_cast<__node_base_pointer>(__prior.__ptr_)->__right_;
            }
        }
        // __v < *prev(__hint)
        return __find_leaf_high(__parent, __v);
    }
    // else __v > *__hint
    return __find_leaf_low(__parent, __v);
}

// Find place to insert if __v doesn't exist
// Set __parent to parent of null leaf
// Return reference to null leaf
// If __v exists, set parent to node of __v and return reference to node of __v
template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_equal(__parent_pointer& __parent,
                                                const _Key& __v)
{
    __node_pointer __nd = __root();
    __node_base_pointer* __nd_ptr = __root_ptr();
    if (__nd != nullptr)
    {
        while (true)
        {
            if (value_comp()(__v, __nd->__value_))
            {
                if (__nd->__left_ != nullptr) {
                    __nd_ptr = _VSTD::addressof(__nd->__left_);
                    __nd = static_cast<__node_pointer>(__nd->__left_);
                } else {
                    __parent = static_cast<__parent_pointer>(__nd);
                    return __parent->__left_;
                }
            }
            else if (value_comp()(__nd->__value_, __v))
            {
                if (__nd->__right_ != nullptr) {
                    __nd_ptr = _VSTD::addressof(__nd->__right_);
                    __nd = static_cast<__node_pointer>(__nd->__right_);
                } else {
                    __parent = static_cast<__parent_pointer>(__nd);
                    return __nd->__right_;
                }
            }
            else
            {
                __parent = static_cast<__parent_pointer>(__nd);
                return *__nd_ptr;
            }
        }
    }
    __parent = static_cast<__parent_pointer>(__end_node());
    return __parent->__left_;
}

// Find place to insert if __v doesn't exist
// First check prior to __hint.
// Next check after __hint.
// Next do O(log N) search.
// Set __parent to parent of null leaf
// Return reference to null leaf
// If __v exists, set parent to node of __v and return reference to node of __v
template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_equal(const_iterator __hint,
                                                __parent_pointer& __parent,
                                                __node_base_pointer& __dummy,
                                                const _Key& __v)
{
    if (__hint == end() || value_comp()(__v, *__hint))  // check before
    {
        // __v < *__hint
        const_iterator __prior = __hint;
        if (__prior == begin() || value_comp()(*--__prior, __v))
        {
            // *prev(__hint) < __v < *__hint
            if (__hint.__ptr_->__left_ == nullptr)
            {
                __parent = static_cast<__parent_pointer>(__hint.__ptr_);
                return __parent->__left_;
            }
            else
            {
                __parent = static_cast<__parent_pointer>(__prior.__ptr_);
                return static_cast<__node_base_pointer>(__prior.__ptr_)->__right_;
            }
        }
        // __v <= *prev(__hint)
        return __find_equal(__parent, __v);
    }
    else if (value_comp()(*__hint, __v))  // check after
    {
        // *__hint < __v
        const_iterator __next = _VSTD::next(__hint);
        if (__next == end() || value_comp()(__v, *__next))
        {
            // *__hint < __v < *_VSTD::next(__hint)
            if (__hint.__get_np()->__right_ == nullptr)
            {
                __parent = static_cast<__parent_pointer>(__hint.__ptr_);
                return static_cast<__node_base_pointer>(__hint.__ptr_)->__right_;
            }
            else
            {
                __parent = static_cast<__parent_pointer>(__next.__ptr_);
                return __parent->__left_;
            }
        }
        // *next(__hint) <= __v
        return __find_equal(__parent, __v);
    }
    // else __v == *__hint
    __parent = static_cast<__parent_pointer>(__hint.__ptr_);
    __dummy = static_cast<__node_base_pointer>(__hint.__ptr_);
    return __dummy;
}

template <class _Tp, class _Compare, class _Allocator>
void __tree<_Tp, _Compare, _Allocator>::__insert_node_at(
    __parent_pointer __parent, __node_base_pointer& __child,
    __node_base_pointer __new_node) _NOEXCEPT
{
    __new_node->__left_   = nullptr;
    __new_node->__right_  = nullptr;
    __new_node->__parent_ = __parent;
    // __new_node->__is_black_ is initialized in __tree_balance_after_insert
    __child = __new_node;
    if (__begin_node()->__left_ != nullptr)
        __begin_node() = static_cast<__iter_pointer>(__begin_node()->__left_);
    __tree_balance_after_insert(__end_node()->__left_, __child);
    ++size();
}

#ifndef _LIBCPP_CXX03_LANG
template <class _Tp, class _Compare, class _Allocator>
template <class _Key, class... _Args>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__emplace_unique_key_args(_Key const& __k, _Args&&... __args)
#else
template <class _Tp, class _Compare, class _Allocator>
template <class _Key, class _Args>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__emplace_unique_key_args(_Key const& __k, _Args& __args)
#endif
{
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_equal(__parent, __k);
    __node_pointer __r = static_cast<__node_pointer>(__child);
    bool __inserted = false;
    if (__child == nullptr)
    {
#ifndef _LIBCPP_CXX03_LANG
        __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
#else
        __node_holder __h = __construct_node(__args);
#endif
        __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
        __r = __h.release();
        __inserted = true;
    }
    return pair<iterator, bool>(iterator(__r), __inserted);
}


#ifndef _LIBCPP_CXX03_LANG
template <class _Tp, class _Compare, class _Allocator>
template <class _Key, class... _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_hint_unique_key_args(
    const_iterator __p, _Key const& __k, _Args&&... __args)
#else
template <class _Tp, class _Compare, class _Allocator>
template <class _Key, class _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_hint_unique_key_args(
    const_iterator __p, _Key const& __k, _Args& __args)
#endif
{
    __parent_pointer __parent;
    __node_base_pointer __dummy;
    __node_base_pointer& __child = __find_equal(__p, __parent, __dummy, __k);
    __node_pointer __r = static_cast<__node_pointer>(__child);
    if (__child == nullptr)
    {
#ifndef _LIBCPP_CXX03_LANG
        __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
#else
        __node_holder __h = __construct_node(__args);
#endif
        __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
        __r = __h.release();
    }
    return iterator(__r);
}


#ifndef _LIBCPP_CXX03_LANG

template <class _Tp, class _Compare, class _Allocator>
template <class ..._Args>
typename __tree<_Tp, _Compare, _Allocator>::__node_holder
__tree<_Tp, _Compare, _Allocator>::__construct_node(_Args&& ...__args)
{
    static_assert(!__is_tree_value_type<_Args...>::value,
                  "Cannot construct from __value_type");
    __node_allocator& __na = __node_alloc();
    __node_holder __h(__node_traits::allocate(__na, 1), _Dp(__na));
    __node_traits::construct(__na, _NodeTypes::__get_ptr(__h->__value_), _VSTD::forward<_Args>(__args)...);
    __h.get_deleter().__value_constructed = true;
    return __h;
}


template <class _Tp, class _Compare, class _Allocator>
template <class... _Args>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__emplace_unique_impl(_Args&&... __args)
{
    __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_equal(__parent, __h->__value_);
    __node_pointer __r = static_cast<__node_pointer>(__child);
    bool __inserted = false;
    if (__child == nullptr)
    {
        __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
        __r = __h.release();
        __inserted = true;
    }
    return pair<iterator, bool>(iterator(__r), __inserted);
}

template <class _Tp, class _Compare, class _Allocator>
template <class... _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_hint_unique_impl(const_iterator __p, _Args&&... __args)
{
    __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
    __parent_pointer __parent;
    __node_base_pointer __dummy;
    __node_base_pointer& __child = __find_equal(__p, __parent, __dummy, __h->__value_);
    __node_pointer __r = static_cast<__node_pointer>(__child);
    if (__child == nullptr)
    {
        __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
        __r = __h.release();
    }
    return iterator(__r);
}

template <class _Tp, class _Compare, class _Allocator>
template <class... _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_multi(_Args&&... __args)
{
    __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_leaf_high(__parent, _NodeTypes::__get_key(__h->__value_));
    __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
    return iterator(static_cast<__node_pointer>(__h.release()));
}

template <class _Tp, class _Compare, class _Allocator>
template <class... _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_hint_multi(const_iterator __p,
                                                        _Args&&... __args)
{
    __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_leaf(__p, __parent, _NodeTypes::__get_key(__h->__value_));
    __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
    return iterator(static_cast<__node_pointer>(__h.release()));
}


#else  // _LIBCPP_CXX03_LANG

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_holder
__tree<_Tp, _Compare, _Allocator>::__construct_node(const __container_value_type& __v)
{
    __node_allocator& __na = __node_alloc();
    __node_holder __h(__node_traits::allocate(__na, 1), _Dp(__na));
    __node_traits::construct(__na, _NodeTypes::__get_ptr(__h->__value_), __v);
    __h.get_deleter().__value_constructed = true;
    return _LIBCPP_EXPLICIT_MOVE(__h);  // explicitly moved for C++03
}

#endif  // _LIBCPP_CXX03_LANG

#ifdef _LIBCPP_CXX03_LANG
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__insert_multi(const __container_value_type& __v)
{
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_leaf_high(__parent, _NodeTypes::__get_key(__v));
    __node_holder __h = __construct_node(__v);
    __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
    return iterator(__h.release());
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__insert_multi(const_iterator __p, const __container_value_type& __v)
{
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_leaf(__p, __parent, _NodeTypes::__get_key(__v));
    __node_holder __h = __construct_node(__v);
    __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
    return iterator(__h.release());
}
#endif

template <class _Tp, class _Compare, class _Allocator>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__node_assign_unique(const __container_value_type& __v, __node_pointer __nd)
{
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_equal(__parent, _NodeTypes::__get_key(__v));
    __node_pointer __r = static_cast<__node_pointer>(__child);
    bool __inserted = false;
    if (__child == nullptr)
    {
        __nd->__value_ = __v;
        __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__nd));
        __r = __nd;
        __inserted = true;
    }
    return pair<iterator, bool>(iterator(__r), __inserted);
}


template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__node_insert_multi(__node_pointer __nd)
{
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_leaf_high(__parent, _NodeTypes::__get_key(__nd->__value_));
    __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__nd));
    return iterator(__nd);
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__node_insert_multi(const_iterator __p,
                                                       __node_pointer __nd)
{
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_leaf(__p, __parent, _NodeTypes::__get_key(__nd->__value_));
    __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__nd));
    return iterator(__nd);
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__remove_node_pointer(__node_pointer __ptr) _NOEXCEPT
{
    iterator __r(__ptr);
    ++__r;
    if (__begin_node() == __ptr)
        __begin_node() = __r.__ptr_;
    --size();
    __tree_remove(__end_node()->__left_,
                  static_cast<__node_base_pointer>(__ptr));
    return __r;
}

#if _LIBCPP_STD_VER > 14
template <class _Tp, class _Compare, class _Allocator>
template <class _NodeHandle, class _InsertReturnType>
_LIBCPP_INLINE_VISIBILITY
_InsertReturnType
__tree<_Tp, _Compare, _Allocator>::__node_handle_insert_unique(
    _NodeHandle&& __nh)
{
    if (__nh.empty())
        return _InsertReturnType{end(), false, _NodeHandle()};

    __node_pointer __ptr = __nh.__ptr_;
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_equal(__parent,
                                                __ptr->__value_);
    if (__child != nullptr)
        return _InsertReturnType{
            iterator(static_cast<__node_pointer>(__child)),
            false, _VSTD::move(__nh)};

    __insert_node_at(__parent, __child,
                     static_cast<__node_base_pointer>(__ptr));
    __nh.__release_ptr();
    return _InsertReturnType{iterator(__ptr), true, _NodeHandle()};
}

template <class _Tp, class _Compare, class _Allocator>
template <class _NodeHandle>
_LIBCPP_INLINE_VISIBILITY
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__node_handle_insert_unique(
    const_iterator __hint, _NodeHandle&& __nh)
{
    if (__nh.empty())
        return end();

    __node_pointer __ptr = __nh.__ptr_;
    __parent_pointer __parent;
    __node_base_pointer __dummy;
    __node_base_pointer& __child = __find_equal(__hint, __parent, __dummy,
                                                __ptr->__value_);
    __node_pointer __r = static_cast<__node_pointer>(__child);
    if (__child == nullptr)
    {
        __insert_node_at(__parent, __child,
                         static_cast<__node_base_pointer>(__ptr));
        __r = __ptr;
        __nh.__release_ptr();
    }
    return iterator(__r);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _NodeHandle>
_LIBCPP_INLINE_VISIBILITY
_NodeHandle
__tree<_Tp, _Compare, _Allocator>::__node_handle_extract(key_type const& __key)
{
    iterator __it = find(__key);
    if (__it == end())
        return _NodeHandle();
    return __node_handle_extract<_NodeHandle>(__it);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _NodeHandle>
_LIBCPP_INLINE_VISIBILITY
_NodeHandle
__tree<_Tp, _Compare, _Allocator>::__node_handle_extract(const_iterator __p)
{
    __node_pointer __np = __p.__get_np();
    __remove_node_pointer(__np);
    return _NodeHandle(__np, __alloc());
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Tree>
_LIBCPP_INLINE_VISIBILITY
void
__tree<_Tp, _Compare, _Allocator>::__node_handle_merge_unique(_Tree& __source)
{
    static_assert(is_same<typename _Tree::__node_pointer, __node_pointer>::value, "");

    for (typename _Tree::iterator __i = __source.begin();
         __i != __source.end();)
    {
        __node_pointer __src_ptr = __i.__get_np();
        __parent_pointer __parent;
        __node_base_pointer& __child =
            __find_equal(__parent, _NodeTypes::__get_key(__src_ptr->__value_));
        ++__i;
        if (__child != nullptr)
            continue;
        __source.__remove_node_pointer(__src_ptr);
        __insert_node_at(__parent, __child,
                         static_cast<__node_base_pointer>(__src_ptr));
    }
}

template <class _Tp, class _Compare, class _Allocator>
template <class _NodeHandle>
_LIBCPP_INLINE_VISIBILITY
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__node_handle_insert_multi(_NodeHandle&& __nh)
{
    if (__nh.empty())
        return end();
    __node_pointer __ptr = __nh.__ptr_;
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_leaf_high(
        __parent, _NodeTypes::__get_key(__ptr->__value_));
    __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__ptr));
    __nh.__release_ptr();
    return iterator(__ptr);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _NodeHandle>
_LIBCPP_INLINE_VISIBILITY
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__node_handle_insert_multi(
    const_iterator __hint, _NodeHandle&& __nh)
{
    if (__nh.empty())
        return end();

    __node_pointer __ptr = __nh.__ptr_;
    __parent_pointer __parent;
    __node_base_pointer& __child = __find_leaf(__hint, __parent,
                                               _NodeTypes::__get_key(__ptr->__value_));
    __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__ptr));
    __nh.__release_ptr();
    return iterator(__ptr);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Tree>
_LIBCPP_INLINE_VISIBILITY
void
__tree<_Tp, _Compare, _Allocator>::__node_handle_merge_multi(_Tree& __source)
{
    static_assert(is_same<typename _Tree::__node_pointer, __node_pointer>::value, "");

    for (typename _Tree::iterator __i = __source.begin();
         __i != __source.end();)
    {
        __node_pointer __src_ptr = __i.__get_np();
        __parent_pointer __parent;
        __node_base_pointer& __child = __find_leaf_high(
            __parent, _NodeTypes::__get_key(__src_ptr->__value_));
        ++__i;
        __source.__remove_node_pointer(__src_ptr);
        __insert_node_at(__parent, __child,
                         static_cast<__node_base_pointer>(__src_ptr));
    }
}

#endif  // _LIBCPP_STD_VER > 14

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::erase(const_iterator __p)
{
    __node_pointer __np = __p.__get_np();
    iterator __r = __remove_node_pointer(__np);
    __node_allocator& __na = __node_alloc();
    __node_traits::destroy(__na, _NodeTypes::__get_ptr(
        const_cast<__node_value_type&>(*__p)));
    __node_traits::deallocate(__na, __np, 1);
    return __r;
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::erase(const_iterator __f, const_iterator __l)
{
    while (__f != __l)
        __f = erase(__f);
    return iterator(__l.__ptr_);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::size_type
__tree<_Tp, _Compare, _Allocator>::__erase_unique(const _Key& __k)
{
    iterator __i = find(__k);
    if (__i == end())
        return 0;
    erase(__i);
    return 1;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::size_type
__tree<_Tp, _Compare, _Allocator>::__erase_multi(const _Key& __k)
{
    pair<iterator, iterator> __p = __equal_range_multi(__k);
    size_type __r = 0;
    for (; __p.first != __p.second; ++__r)
        __p.first = erase(__p.first);
    return __r;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::find(const _Key& __v)
{
    iterator __p = __lower_bound(__v, __root(), __end_node());
    if (__p != end() && !value_comp()(__v, *__p))
        return __p;
    return end();
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::const_iterator
__tree<_Tp, _Compare, _Allocator>::find(const _Key& __v) const
{
    const_iterator __p = __lower_bound(__v, __root(), __end_node());
    if (__p != end() && !value_comp()(__v, *__p))
        return __p;
    return end();
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::size_type
__tree<_Tp, _Compare, _Allocator>::__count_unique(const _Key& __k) const
{
    __node_pointer __rt = __root();
    while (__rt != nullptr)
    {
        if (value_comp()(__k, __rt->__value_))
        {
            __rt = static_cast<__node_pointer>(__rt->__left_);
        }
        else if (value_comp()(__rt->__value_, __k))
            __rt = static_cast<__node_pointer>(__rt->__right_);
        else
            return 1;
    }
    return 0;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::size_type
__tree<_Tp, _Compare, _Allocator>::__count_multi(const _Key& __k) const
{
    __iter_pointer __result = __end_node();
    __node_pointer __rt = __root();
    while (__rt != nullptr)
    {
        if (value_comp()(__k, __rt->__value_))
        {
            __result = static_cast<__iter_pointer>(__rt);
            __rt = static_cast<__node_pointer>(__rt->__left_);
        }
        else if (value_comp()(__rt->__value_, __k))
            __rt = static_cast<__node_pointer>(__rt->__right_);
        else
            return _VSTD::distance(
                __lower_bound(__k, static_cast<__node_pointer>(__rt->__left_), static_cast<__iter_pointer>(__rt)),
                __upper_bound(__k, static_cast<__node_pointer>(__rt->__right_), __result)
            );
    }
    return 0;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__lower_bound(const _Key& __v,
                                                 __node_pointer __root,
                                                 __iter_pointer __result)
{
    while (__root != nullptr)
    {
        if (!value_comp()(__root->__value_, __v))
        {
            __result = static_cast<__iter_pointer>(__root);
            __root = static_cast<__node_pointer>(__root->__left_);
        }
        else
            __root = static_cast<__node_pointer>(__root->__right_);
    }
    return iterator(__result);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::const_iterator
__tree<_Tp, _Compare, _Allocator>::__lower_bound(const _Key& __v,
                                                 __node_pointer __root,
                                                 __iter_pointer __result) const
{
    while (__root != nullptr)
    {
        if (!value_comp()(__root->__value_, __v))
        {
            __result = static_cast<__iter_pointer>(__root);
            __root = static_cast<__node_pointer>(__root->__left_);
        }
        else
            __root = static_cast<__node_pointer>(__root->__right_);
    }
    return const_iterator(__result);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__upper_bound(const _Key& __v,
                                                 __node_pointer __root,
                                                 __iter_pointer __result)
{
    while (__root != nullptr)
    {
        if (value_comp()(__v, __root->__value_))
        {
            __result = static_cast<__iter_pointer>(__root);
            __root = static_cast<__node_pointer>(__root->__left_);
        }
        else
            __root = static_cast<__node_pointer>(__root->__right_);
    }
    return iterator(__result);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::const_iterator
__tree<_Tp, _Compare, _Allocator>::__upper_bound(const _Key& __v,
                                                 __node_pointer __root,
                                                 __iter_pointer __result) const
{
    while (__root != nullptr)
    {
        if (value_comp()(__v, __root->__value_))
        {
            __result = static_cast<__iter_pointer>(__root);
            __root = static_cast<__node_pointer>(__root->__left_);
        }
        else
            __root = static_cast<__node_pointer>(__root->__right_);
    }
    return const_iterator(__result);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator,
     typename __tree<_Tp, _Compare, _Allocator>::iterator>
__tree<_Tp, _Compare, _Allocator>::__equal_range_unique(const _Key& __k)
{
    typedef pair<iterator, iterator> _Pp;
    __iter_pointer __result = __end_node();
    __node_pointer __rt = __root();
    while (__rt != nullptr)
    {
        if (value_comp()(__k, __rt->__value_))
        {
            __result = static_cast<__iter_pointer>(__rt);
            __rt = static_cast<__node_pointer>(__rt->__left_);
        }
        else if (value_comp()(__rt->__value_, __k))
            __rt = static_cast<__node_pointer>(__rt->__right_);
        else
            return _Pp(iterator(__rt),
                      iterator(
                          __rt->__right_ != nullptr ?
                              static_cast<__iter_pointer>(__tree_min(__rt->__right_))
                            : __result));
    }
    return _Pp(iterator(__result), iterator(__result));
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
pair<typename __tree<_Tp, _Compare, _Allocator>::const_iterator,
     typename __tree<_Tp, _Compare, _Allocator>::const_iterator>
__tree<_Tp, _Compare, _Allocator>::__equal_range_unique(const _Key& __k) const
{
    typedef pair<const_iterator, const_iterator> _Pp;
    __iter_pointer __result = __end_node();
    __node_pointer __rt = __root();
    while (__rt != nullptr)
    {
        if (value_comp()(__k, __rt->__value_))
        {
            __result = static_cast<__iter_pointer>(__rt);
            __rt = static_cast<__node_pointer>(__rt->__left_);
        }
        else if (value_comp()(__rt->__value_, __k))
            __rt = static_cast<__node_pointer>(__rt->__right_);
        else
            return _Pp(const_iterator(__rt),
                      const_iterator(
                          __rt->__right_ != nullptr ?
                              static_cast<__iter_pointer>(__tree_min(__rt->__right_))
                            : __result));
    }
    return _Pp(const_iterator(__result), const_iterator(__result));
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator,
     typename __tree<_Tp, _Compare, _Allocator>::iterator>
__tree<_Tp, _Compare, _Allocator>::__equal_range_multi(const _Key& __k)
{
    typedef pair<iterator, iterator> _Pp;
    __iter_pointer __result = __end_node();
    __node_pointer __rt = __root();
    while (__rt != nullptr)
    {
        if (value_comp()(__k, __rt->__value_))
        {
            __result = static_cast<__iter_pointer>(__rt);
            __rt = static_cast<__node_pointer>(__rt->__left_);
        }
        else if (value_comp()(__rt->__value_, __k))
            __rt = static_cast<__node_pointer>(__rt->__right_);
        else
            return _Pp(__lower_bound(__k, static_cast<__node_pointer>(__rt->__left_), static_cast<__iter_pointer>(__rt)),
                      __upper_bound(__k, static_cast<__node_pointer>(__rt->__right_), __result));
    }
    return _Pp(iterator(__result), iterator(__result));
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
pair<typename __tree<_Tp, _Compare, _Allocator>::const_iterator,
     typename __tree<_Tp, _Compare, _Allocator>::const_iterator>
__tree<_Tp, _Compare, _Allocator>::__equal_range_multi(const _Key& __k) const
{
    typedef pair<const_iterator, const_iterator> _Pp;
    __iter_pointer __result = __end_node();
    __node_pointer __rt = __root();
    while (__rt != nullptr)
    {
        if (value_comp()(__k, __rt->__value_))
        {
            __result = static_cast<__iter_pointer>(__rt);
            __rt = static_cast<__node_pointer>(__rt->__left_);
        }
        else if (value_comp()(__rt->__value_, __k))
            __rt = static_cast<__node_pointer>(__rt->__right_);
        else
            return _Pp(__lower_bound(__k, static_cast<__node_pointer>(__rt->__left_), static_cast<__iter_pointer>(__rt)),
                      __upper_bound(__k, static_cast<__node_pointer>(__rt->__right_), __result));
    }
    return _Pp(const_iterator(__result), const_iterator(__result));
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_holder
__tree<_Tp, _Compare, _Allocator>::remove(const_iterator __p) _NOEXCEPT
{
    __node_pointer __np = __p.__get_np();
    if (__begin_node() == __p.__ptr_)
    {
        if (__np->__right_ != nullptr)
            __begin_node() = static_cast<__iter_pointer>(__np->__right_);
        else
            __begin_node() = static_cast<__iter_pointer>(__np->__parent_);
    }
    --size();
    __tree_remove(__end_node()->__left_,
                  static_cast<__node_base_pointer>(__np));
    return __node_holder(__np, _Dp(__node_alloc(), true));
}

template <class _Tp, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
void
swap(__tree<_Tp, _Compare, _Allocator>& __x,
     __tree<_Tp, _Compare, _Allocator>& __y)
    _NOEXCEPT_(_NOEXCEPT_(__x.swap(__y)))
{
    __x.swap(__y);
}

_LIBCPP_END_NAMESPACE_STD

_LIBCPP_POP_MACROS

#endif  // _LIBCPP___TREE