***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000827 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The decimal representation of a binary word with a leading 1. This statistic is obtained by prepending $1$ to the binary word and interpreting it as a number in binary. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(w): return Integer("0b1" + str(w)) ----------------------------------------------------------------------------- Statistic values: 0 => 2 1 => 3 00 => 4 01 => 5 10 => 6 11 => 7 000 => 8 001 => 9 010 => 10 011 => 11 100 => 12 101 => 13 110 => 14 111 => 15 0000 => 16 0001 => 17 0010 => 18 0011 => 19 0100 => 20 0101 => 21 0110 => 22 0111 => 23 1000 => 24 1001 => 25 1010 => 26 1011 => 27 1100 => 28 1101 => 29 1110 => 30 1111 => 31 00000 => 32 00001 => 33 00010 => 34 00011 => 35 00100 => 36 00101 => 37 00110 => 38 00111 => 39 01000 => 40 01001 => 41 01010 => 42 01011 => 43 01100 => 44 01101 => 45 01110 => 46 01111 => 47 10000 => 48 10001 => 49 10010 => 50 10011 => 51 10100 => 52 10101 => 53 10110 => 54 10111 => 55 11000 => 56 11001 => 57 11010 => 58 11011 => 59 11100 => 60 11101 => 61 11110 => 62 11111 => 63 000000 => 64 000001 => 65 000010 => 66 000011 => 67 000100 => 68 000101 => 69 000110 => 70 000111 => 71 001000 => 72 001001 => 73 001010 => 74 001011 => 75 001100 => 76 001101 => 77 001110 => 78 001111 => 79 010000 => 80 010001 => 81 010010 => 82 010011 => 83 010100 => 84 010101 => 85 010110 => 86 010111 => 87 011000 => 88 011001 => 89 011010 => 90 011011 => 91 011100 => 92 011101 => 93 011110 => 94 011111 => 95 100000 => 96 100001 => 97 100010 => 98 100011 => 99 100100 => 100 100101 => 101 100110 => 102 100111 => 103 101000 => 104 101001 => 105 101010 => 106 101011 => 107 101100 => 108 101101 => 109 101110 => 110 101111 => 111 110000 => 112 110001 => 113 110010 => 114 110011 => 115 110100 => 116 110101 => 117 110110 => 118 110111 => 119 111000 => 120 111001 => 121 111010 => 122 111011 => 123 111100 => 124 111101 => 125 111110 => 126 111111 => 127 0000000 => 128 0000001 => 129 0000010 => 130 0000011 => 131 0000100 => 132 0000101 => 133 0000110 => 134 0000111 => 135 0001000 => 136 0001001 => 137 0001010 => 138 0001011 => 139 0001100 => 140 0001101 => 141 0001110 => 142 0001111 => 143 0010000 => 144 0010001 => 145 0010010 => 146 0010011 => 147 0010100 => 148 0010101 => 149 0010110 => 150 0010111 => 151 0011000 => 152 0011001 => 153 0011010 => 154 0011011 => 155 0011100 => 156 0011101 => 157 0011110 => 158 0011111 => 159 0100000 => 160 0100001 => 161 0100010 => 162 0100011 => 163 0100100 => 164 0100101 => 165 0100110 => 166 0100111 => 167 0101000 => 168 0101001 => 169 0101010 => 170 0101011 => 171 0101100 => 172 0101101 => 173 0101110 => 174 0101111 => 175 0110000 => 176 0110001 => 177 0110010 => 178 0110011 => 179 0110100 => 180 0110101 => 181 0110110 => 182 0110111 => 183 0111000 => 184 0111001 => 185 0111010 => 186 0111011 => 187 0111100 => 188 0111101 => 189 0111110 => 190 0111111 => 191 1000000 => 192 1000001 => 193 1000010 => 194 1000011 => 195 1000100 => 196 1000101 => 197 1000110 => 198 1000111 => 199 1001000 => 200 1001001 => 201 1001010 => 202 1001011 => 203 1001100 => 204 1001101 => 205 1001110 => 206 1001111 => 207 1010000 => 208 1010001 => 209 1010010 => 210 1010011 => 211 1010100 => 212 1010101 => 213 1010110 => 214 1010111 => 215 1011000 => 216 1011001 => 217 1011010 => 218 1011011 => 219 1011100 => 220 1011101 => 221 1011110 => 222 1011111 => 223 1100000 => 224 1100001 => 225 1100010 => 226 1100011 => 227 1100100 => 228 1100101 => 229 1100110 => 230 1100111 => 231 1101000 => 232 1101001 => 233 1101010 => 234 1101011 => 235 1101100 => 236 1101101 => 237 1101110 => 238 1101111 => 239 1110000 => 240 1110001 => 241 1110010 => 242 1110011 => 243 1110100 => 244 1110101 => 245 1110110 => 246 1110111 => 247 1111000 => 248 1111001 => 249 1111010 => 250 1111011 => 251 1111100 => 252 1111101 => 253 1111110 => 254 1111111 => 255 00000000 => 256 00000001 => 257 00000010 => 258 00000011 => 259 00000100 => 260 00000101 => 261 00000110 => 262 00000111 => 263 00001000 => 264 00001001 => 265 00001010 => 266 00001011 => 267 00001100 => 268 00001101 => 269 00001110 => 270 00001111 => 271 00010000 => 272 00010001 => 273 00010010 => 274 00010011 => 275 00010100 => 276 00010101 => 277 00010110 => 278 00010111 => 279 00011000 => 280 00011001 => 281 00011010 => 282 00011011 => 283 00011100 => 284 00011101 => 285 00011110 => 286 00011111 => 287 00100000 => 288 00100001 => 289 00100010 => 290 00100011 => 291 00100100 => 292 00100101 => 293 00100110 => 294 00100111 => 295 00101000 => 296 00101001 => 297 00101010 => 298 00101011 => 299 00101100 => 300 00101101 => 301 00101110 => 302 00101111 => 303 00110000 => 304 00110001 => 305 00110010 => 306 00110011 => 307 00110100 => 308 00110101 => 309 00110110 => 310 00110111 => 311 00111000 => 312 00111001 => 313 00111010 => 314 00111011 => 315 00111100 => 316 00111101 => 317 00111110 => 318 00111111 => 319 01000000 => 320 01000001 => 321 01000010 => 322 01000011 => 323 01000100 => 324 01000101 => 325 01000110 => 326 01000111 => 327 01001000 => 328 01001001 => 329 01001010 => 330 01001011 => 331 01001100 => 332 01001101 => 333 01001110 => 334 01001111 => 335 01010000 => 336 01010001 => 337 01010010 => 338 01010011 => 339 01010100 => 340 01010101 => 341 01010110 => 342 01010111 => 343 01011000 => 344 01011001 => 345 01011010 => 346 01011011 => 347 01011100 => 348 01011101 => 349 01011110 => 350 01011111 => 351 01100000 => 352 01100001 => 353 01100010 => 354 01100011 => 355 01100100 => 356 01100101 => 357 01100110 => 358 01100111 => 359 01101000 => 360 01101001 => 361 01101010 => 362 01101011 => 363 01101100 => 364 01101101 => 365 01101110 => 366 01101111 => 367 01110000 => 368 01110001 => 369 01110010 => 370 01110011 => 371 01110100 => 372 01110101 => 373 01110110 => 374 01110111 => 375 01111000 => 376 01111001 => 377 01111010 => 378 01111011 => 379 01111100 => 380 01111101 => 381 01111110 => 382 01111111 => 383 10000000 => 384 10000001 => 385 10000010 => 386 10000011 => 387 10000100 => 388 10000101 => 389 10000110 => 390 10000111 => 391 10001000 => 392 10001001 => 393 10001010 => 394 10001011 => 395 10001100 => 396 10001101 => 397 10001110 => 398 10001111 => 399 10010000 => 400 10010001 => 401 10010010 => 402 10010011 => 403 10010100 => 404 10010101 => 405 10010110 => 406 10010111 => 407 10011000 => 408 10011001 => 409 10011010 => 410 10011011 => 411 10011100 => 412 10011101 => 413 10011110 => 414 10011111 => 415 10100000 => 416 10100001 => 417 10100010 => 418 10100011 => 419 10100100 => 420 10100101 => 421 10100110 => 422 10100111 => 423 10101000 => 424 10101001 => 425 10101010 => 426 10101011 => 427 10101100 => 428 10101101 => 429 10101110 => 430 10101111 => 431 10110000 => 432 10110001 => 433 10110010 => 434 10110011 => 435 10110100 => 436 10110101 => 437 10110110 => 438 10110111 => 439 10111000 => 440 10111001 => 441 10111010 => 442 10111011 => 443 10111100 => 444 10111101 => 445 10111110 => 446 10111111 => 447 11000000 => 448 11000001 => 449 11000010 => 450 11000011 => 451 11000100 => 452 11000101 => 453 11000110 => 454 11000111 => 455 11001000 => 456 11001001 => 457 11001010 => 458 11001011 => 459 11001100 => 460 11001101 => 461 11001110 => 462 11001111 => 463 11010000 => 464 11010001 => 465 11010010 => 466 11010011 => 467 11010100 => 468 11010101 => 469 11010110 => 470 11010111 => 471 11011000 => 472 11011001 => 473 11011010 => 474 11011011 => 475 11011100 => 476 11011101 => 477 11011110 => 478 11011111 => 479 11100000 => 480 11100001 => 481 11100010 => 482 11100011 => 483 11100100 => 484 11100101 => 485 11100110 => 486 11100111 => 487 11101000 => 488 11101001 => 489 11101010 => 490 11101011 => 491 11101100 => 492 11101101 => 493 11101110 => 494 11101111 => 495 11110000 => 496 11110001 => 497 11110010 => 498 11110011 => 499 11110100 => 500 11110101 => 501 11110110 => 502 11110111 => 503 11111000 => 504 11111001 => 505 11111010 => 506 11111011 => 507 11111100 => 508 11111101 => 509 11111110 => 510 11111111 => 511 000000000 => 512 000000001 => 513 000000010 => 514 000000011 => 515 000000100 => 516 000000101 => 517 000000110 => 518 000000111 => 519 000001000 => 520 000001001 => 521 000001010 => 522 000001011 => 523 000001100 => 524 000001101 => 525 000001110 => 526 000001111 => 527 000010000 => 528 000010001 => 529 000010010 => 530 000010011 => 531 000010100 => 532 000010101 => 533 000010110 => 534 000010111 => 535 000011000 => 536 000011001 => 537 000011010 => 538 000011011 => 539 000011100 => 540 000011101 => 541 000011110 => 542 000011111 => 543 000100000 => 544 000100001 => 545 000100010 => 546 000100011 => 547 000100100 => 548 000100101 => 549 000100110 => 550 000100111 => 551 000101000 => 552 000101001 => 553 000101010 => 554 000101011 => 555 000101100 => 556 000101101 => 557 000101110 => 558 000101111 => 559 000110000 => 560 000110001 => 561 000110010 => 562 000110011 => 563 000110100 => 564 000110101 => 565 000110110 => 566 000110111 => 567 000111000 => 568 000111001 => 569 000111010 => 570 000111011 => 571 000111100 => 572 000111101 => 573 000111110 => 574 000111111 => 575 001000000 => 576 001000001 => 577 001000010 => 578 001000011 => 579 001000100 => 580 001000101 => 581 001000110 => 582 001000111 => 583 001001000 => 584 001001001 => 585 001001010 => 586 001001011 => 587 001001100 => 588 001001101 => 589 001001110 => 590 001001111 => 591 001010000 => 592 001010001 => 593 001010010 => 594 001010011 => 595 001010100 => 596 001010101 => 597 001010110 => 598 001010111 => 599 001011000 => 600 001011001 => 601 001011010 => 602 001011011 => 603 001011100 => 604 001011101 => 605 001011110 => 606 001011111 => 607 001100000 => 608 001100001 => 609 001100010 => 610 001100011 => 611 001100100 => 612 001100101 => 613 001100110 => 614 001100111 => 615 001101000 => 616 001101001 => 617 001101010 => 618 001101011 => 619 001101100 => 620 001101101 => 621 001101110 => 622 001101111 => 623 001110000 => 624 001110001 => 625 001110010 => 626 001110011 => 627 001110100 => 628 001110101 => 629 001110110 => 630 001110111 => 631 001111000 => 632 001111001 => 633 001111010 => 634 001111011 => 635 001111100 => 636 001111101 => 637 001111110 => 638 001111111 => 639 010000000 => 640 010000001 => 641 010000010 => 642 010000011 => 643 010000100 => 644 010000101 => 645 010000110 => 646 010000111 => 647 010001000 => 648 010001001 => 649 010001010 => 650 010001011 => 651 010001100 => 652 010001101 => 653 010001110 => 654 010001111 => 655 010010000 => 656 010010001 => 657 010010010 => 658 010010011 => 659 010010100 => 660 010010101 => 661 010010110 => 662 010010111 => 663 010011000 => 664 010011001 => 665 010011010 => 666 010011011 => 667 010011100 => 668 010011101 => 669 010011110 => 670 010011111 => 671 010100000 => 672 010100001 => 673 010100010 => 674 010100011 => 675 010100100 => 676 010100101 => 677 010100110 => 678 010100111 => 679 010101000 => 680 010101001 => 681 010101010 => 682 010101011 => 683 010101100 => 684 010101101 => 685 010101110 => 686 010101111 => 687 010110000 => 688 010110001 => 689 010110010 => 690 010110011 => 691 010110100 => 692 010110101 => 693 010110110 => 694 010110111 => 695 010111000 => 696 010111001 => 697 010111010 => 698 010111011 => 699 010111100 => 700 010111101 => 701 010111110 => 702 010111111 => 703 011000000 => 704 011000001 => 705 011000010 => 706 011000011 => 707 011000100 => 708 011000101 => 709 011000110 => 710 011000111 => 711 011001000 => 712 011001001 => 713 011001010 => 714 011001011 => 715 011001100 => 716 011001101 => 717 011001110 => 718 011001111 => 719 011010000 => 720 011010001 => 721 011010010 => 722 011010011 => 723 011010100 => 724 011010101 => 725 011010110 => 726 011010111 => 727 011011000 => 728 011011001 => 729 011011010 => 730 011011011 => 731 011011100 => 732 011011101 => 733 011011110 => 734 011011111 => 735 011100000 => 736 011100001 => 737 011100010 => 738 011100011 => 739 011100100 => 740 011100101 => 741 011100110 => 742 011100111 => 743 011101000 => 744 011101001 => 745 011101010 => 746 011101011 => 747 011101100 => 748 011101101 => 749 011101110 => 750 011101111 => 751 011110000 => 752 011110001 => 753 011110010 => 754 011110011 => 755 011110100 => 756 011110101 => 757 011110110 => 758 011110111 => 759 011111000 => 760 011111001 => 761 011111010 => 762 011111011 => 763 011111100 => 764 011111101 => 765 011111110 => 766 011111111 => 767 100000000 => 768 100000001 => 769 100000010 => 770 100000011 => 771 100000100 => 772 100000101 => 773 100000110 => 774 100000111 => 775 100001000 => 776 100001001 => 777 100001010 => 778 100001011 => 779 100001100 => 780 100001101 => 781 100001110 => 782 100001111 => 783 100010000 => 784 100010001 => 785 100010010 => 786 100010011 => 787 100010100 => 788 100010101 => 789 100010110 => 790 100010111 => 791 100011000 => 792 100011001 => 793 100011010 => 794 100011011 => 795 100011100 => 796 100011101 => 797 100011110 => 798 100011111 => 799 100100000 => 800 100100001 => 801 100100010 => 802 100100011 => 803 100100100 => 804 100100101 => 805 100100110 => 806 100100111 => 807 100101000 => 808 100101001 => 809 100101010 => 810 100101011 => 811 100101100 => 812 100101101 => 813 100101110 => 814 100101111 => 815 100110000 => 816 100110001 => 817 100110010 => 818 100110011 => 819 100110100 => 820 100110101 => 821 100110110 => 822 100110111 => 823 100111000 => 824 100111001 => 825 100111010 => 826 100111011 => 827 100111100 => 828 100111101 => 829 100111110 => 830 100111111 => 831 101000000 => 832 101000001 => 833 101000010 => 834 101000011 => 835 101000100 => 836 101000101 => 837 101000110 => 838 101000111 => 839 101001000 => 840 101001001 => 841 101001010 => 842 101001011 => 843 101001100 => 844 101001101 => 845 101001110 => 846 101001111 => 847 101010000 => 848 101010001 => 849 101010010 => 850 101010011 => 851 101010100 => 852 101010101 => 853 101010110 => 854 101010111 => 855 101011000 => 856 101011001 => 857 101011010 => 858 101011011 => 859 101011100 => 860 101011101 => 861 101011110 => 862 101011111 => 863 101100000 => 864 101100001 => 865 101100010 => 866 101100011 => 867 101100100 => 868 101100101 => 869 101100110 => 870 101100111 => 871 101101000 => 872 101101001 => 873 101101010 => 874 101101011 => 875 101101100 => 876 101101101 => 877 101101110 => 878 101101111 => 879 101110000 => 880 101110001 => 881 101110010 => 882 101110011 => 883 101110100 => 884 101110101 => 885 101110110 => 886 101110111 => 887 101111000 => 888 101111001 => 889 101111010 => 890 101111011 => 891 101111100 => 892 101111101 => 893 101111110 => 894 101111111 => 895 110000000 => 896 110000001 => 897 110000010 => 898 110000011 => 899 110000100 => 900 110000101 => 901 110000110 => 902 110000111 => 903 110001000 => 904 110001001 => 905 110001010 => 906 110001011 => 907 110001100 => 908 110001101 => 909 110001110 => 910 110001111 => 911 110010000 => 912 110010001 => 913 110010010 => 914 110010011 => 915 110010100 => 916 110010101 => 917 110010110 => 918 110010111 => 919 110011000 => 920 110011001 => 921 110011010 => 922 110011011 => 923 110011100 => 924 110011101 => 925 110011110 => 926 110011111 => 927 110100000 => 928 110100001 => 929 110100010 => 930 110100011 => 931 110100100 => 932 110100101 => 933 110100110 => 934 110100111 => 935 110101000 => 936 110101001 => 937 110101010 => 938 110101011 => 939 110101100 => 940 110101101 => 941 110101110 => 942 110101111 => 943 110110000 => 944 110110001 => 945 110110010 => 946 110110011 => 947 110110100 => 948 110110101 => 949 110110110 => 950 110110111 => 951 110111000 => 952 110111001 => 953 110111010 => 954 110111011 => 955 110111100 => 956 110111101 => 957 110111110 => 958 110111111 => 959 111000000 => 960 111000001 => 961 111000010 => 962 111000011 => 963 111000100 => 964 111000101 => 965 111000110 => 966 111000111 => 967 111001000 => 968 111001001 => 969 111001010 => 970 111001011 => 971 111001100 => 972 111001101 => 973 111001110 => 974 111001111 => 975 111010000 => 976 111010001 => 977 111010010 => 978 111010011 => 979 111010100 => 980 111010101 => 981 111010110 => 982 111010111 => 983 111011000 => 984 111011001 => 985 111011010 => 986 111011011 => 987 111011100 => 988 111011101 => 989 111011110 => 990 111011111 => 991 111100000 => 992 111100001 => 993 111100010 => 994 111100011 => 995 111100100 => 996 111100101 => 997 111100110 => 998 111100111 => 999 111101000 => 1000 111101001 => 1001 111101010 => 1002 111101011 => 1003 111101100 => 1004 111101101 => 1005 111101110 => 1006 111101111 => 1007 111110000 => 1008 111110001 => 1009 111110010 => 1010 111110011 => 1011 111110100 => 1012 111110101 => 1013 111110110 => 1014 111110111 => 1015 111111000 => 1016 111111001 => 1017 111111010 => 1018 111111011 => 1019 111111100 => 1020 111111101 => 1021 111111110 => 1022 111111111 => 1023 0000000001 => 1025 0010000001 => 1153 0010101101 => 1197 0010101011 => 1195 0010100111 => 1191 0010011101 => 1181 0010011011 => 1179 0010010111 => 1175 0010001111 => 1167 0001110101 => 1141 0001110011 => 1139 0001101101 => 1133 0001101011 => 1131 0001100111 => 1127 0001011101 => 1117 0001011011 => 1115 0001010111 => 1111 0001001111 => 1103 0000111101 => 1085 0000111011 => 1083 0000110111 => 1079 0000101111 => 1071 0000011111 => 1055 0000000000 => 1024 0000000110 => 1030 0000011000 => 1048 0000011110 => 1054 0000010010 => 1042 0001100000 => 1120 0001100110 => 1126 0001111000 => 1144 0001111110 => 1150 0001110010 => 1138 0001001000 => 1096 0001001110 => 1102 0001000010 => 1090 0001011010 => 1114 0010101010 => 1194 0010101000 => 1192 0010101100 => 1196 0010100100 => 1188 0010010100 => 1172 0001010100 => 1108 0010101110 => 1198 0010100000 => 1184 0010000100 => 1156 0000010100 => 1044 0000000010 => 1026 0000001110 => 1038 0000111110 => 1086 0000000100 => 1028 0000001010 => 1034 0000010110 => 1046 0000101110 => 1070 0001011110 => 1118 0001101110 => 1134 0001110110 => 1142 0001111010 => 1146 0001111100 => 1148 0000000101 => 1029 0000001101 => 1037 0000011101 => 1053 0001111101 => 1149 0000001001 => 1033 0000010101 => 1045 0000101101 => 1069 0010110001 => 1201 0001100001 => 1121 0001000001 => 1089 0000111111 => 1087 0001110100 => 1140 0001101100 => 1132 0010011100 => 1180 0001011100 => 1116 0000111100 => 1084 0001101010 => 1130 0010011010 => 1178 0000111010 => 1082 0010100110 => 1190 0010010110 => 1174 0001010110 => 1110 0000110110 => 1078 0010001110 => 1166 0001101001 => 1129 0000110001 => 1073 0000010001 => 1041 0000001100 => 1036 0000011001 => 1049 0000110011 => 1075 0000110100 => 1076 0000000011 => 1027 0000011011 => 1051 0001101111 => 1135 0000110101 => 1077 0010000010 => 1154 0001000011 => 1091 0010011110 => 1182 0001010000 => 1104 0001000100 => 1092 0001010101 => 1109 0001001011 => 1099 0001100011 => 1123 0001110111 => 1143 0010000000 => 1152 0000000111 => 1031 0000001111 => 1039 0001111111 => 1151 0000001011 => 1035 0000010111 => 1047 0001011111 => 1119 0001111001 => 1145 0000011010 => 1050 0000101010 => 1066 0000100101 => 1061 0010010001 => 1169 0010000101 => 1157 0010010101 => 1173 0010010011 => 1171 0000101011 => 1067 0001000111 => 1095 0000100111 => 1063 0010010010 => 1170 0001001010 => 1098 0001001001 => 1097 0001000101 => 1093 0000100011 => 1059 0000100100 => 1060 0000100010 => 1058 0010110000 => 1200 0000011100 => 1052 0000001000 => 1032 0000101100 => 1068 0010101111 => 1199 0000101000 => 1064 0010001000 => 1160 0001001100 => 1100 0001000110 => 1094 0001100100 => 1124 0001100010 => 1122 0000100110 => 1062 0000110010 => 1074 0010010000 => 1168 0001010010 => 1106 0001000000 => 1088 0001011001 => 1113 0001100101 => 1125 0001110001 => 1137 0010011001 => 1177 0010100101 => 1189 0010101001 => 1193 0010011111 => 1183 0000111001 => 1081 0010001101 => 1165 0001001101 => 1101 0001010001 => 1105 0001010011 => 1107 0001111011 => 1147 0010011000 => 1176 0001011000 => 1112 0000100000 => 1056 0010001011 => 1163 0010000111 => 1159 0000010011 => 1043 0010001100 => 1164 0010000110 => 1158 0000110000 => 1072 0000100001 => 1057 0010100011 => 1187 0010100001 => 1185 0000111000 => 1080 0001101000 => 1128 0000010000 => 1040 0000101001 => 1065 0010100010 => 1186 0010001001 => 1161 0010000011 => 1155 0010001010 => 1162 0001110000 => 1136 ----------------------------------------------------------------------------- Created: May 30, 2017 at 21:43 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 30, 2017 at 21:43 by Martin Rubey