Statistics

Problem Statement for "EnclosingRectangle"

Problem Statement

You are given an even number of points in the plane. You want to find a rectangle whose corners have integer coordinates and sides are parallel to the axes, such that at least half of the given points lie in the interior of the rectangle. Return the area of the smallest such rectangle. ("Smallest rectangle" means the rectangle with the smallest area.) Note that if a point lies on the edge of the rectangle, it does not count as being in the interior.

The input is formatted as follows. You are given String[] X and String[] Y. The first thing that you should do is concatenate the elements of X to form a single String. This String contains up to 100 integer numbers without extra leading zeroes, each separated by one or more spaces. The ith number in this String is the x-coordinate of the ith point. Similarly, you should concatenate the elements of Y to form a single String. That String also contains up to 100 integer numbers without extra leading zeroes, each separated by one or more spaces. The ith number in this String is the y-coordinate of the ith point.

Definition

Class:
EnclosingRectangle
Method:
smallestArea
Parameters:
String[], String[]
Returns:
int
Method signature:
int smallestArea(String[] X, String[] Y)
(be sure your method is public)

Notes

  • If a point lies on the edge of a rectangle, it does not count as being in the interior of that rectangle.

Constraints

  • X contains between 1 and 50 elements, inclusive.
  • Each element of X is a String which contains between 0 and 50 characters, inclusive. Each character is a digit ('0'-'9') or a space (' ').
  • The String formed by concatenating the elements of X has no leading or trailing spaces, and consists of a list of integer numbers separated by one or more spaces. Each number in the list is between 0 and 10000, inclusive, and has no extra leading zeroes.
  • Y contains between 1 and 50 elements, inclusive.
  • Each element of Y is a String which contains between 0 and 50 characters, inclusive. Each character is a digit ('0'-'9') or a space (' ').
  • The String formed by concatenating the elements of Y has no leading or trailing spaces, and consists of a list of integer numbers separated by one or more spaces. Each number in the list is between 0 and 10000, inclusive, and has no extra leading zeroes.
  • The number of integers represented in X is the same as the number of integers represented in Y, which is an even number between 2 and 100, inclusive.
  • All points are distinct.

Examples

  1. { "100 200" }

    { "100 200" }

    Returns: 4

    We have two points (100,100) and (200,200). One way to enclose at least one point is to have the rectangle with opposite corners at (99,99) and (101,101). The area of this rectangle is 4.

  2. { "10 11 13 10 11 13" }

    { "5 5 5 15 16 17" }

    Returns: 10

    We have six points (10,5), (11,5), (13,5), (10,15), (11,16), (13,17). The rectangle with opposite corners at (9,4) and (14,6) encloses the first three points. It turns out that no smaller rectangle can enclose at least three of the six given points. The area of this rectangle is 10.

  3. { "5 6 6 7 7 8 8 9" }

    { "7 6 8 5 9 6 8 7" }

    Returns: 16

    These points form a diamond shape

  4. { "4496 6443 2837 557 4098 1083 3466 1250 6126 ", "3135 7598 9274 9180 5128 741 7625 8316 414 ", "9071 8753 5509 1080 2797 906 3805 698 947 ", "8645 9640 2596 6883 1845 9169 3922 4792 7919 ", "7389 9397 4901 1343 3347 6366 9118 3148 780 ", "4541 9479 483 1174 9615 8900 3067 5397 9879 ", "7440 8948 846 8881 7602 6760 3327 5197 9017 ", "5463 6781 2478 6270 5392 9420 9069 3609 6401 ", "1810 6680 6787 9840 1031 1916 5415 1168 5154 ", "2727 8834 9125 3961 4289 4750 5524 5118 5258 ", "2652 7020 9770 5866 3386 6447 7960 3889 2158 ", "6717" }

    { "6801 8243 9390 2156 5505 5509 3442 6663 1294 ", "9979 1008 5644 7516 5442 5909 4550 2431 2779 ", "419 4744 8155 7800 2944 4169 1633 1464 7353 ", "5365 1548 3073 8596 4461 2540 4664 5057 1870 ", "4782 4028 8003 9175 2592 4520 2420 6955 519 ", "2141 1580 5170 9138 4268 9724 1093 5633 9820 ", "3411 9789 6200 7661 2296 8644 8259 8631 4342 ", "574 530 6664 8812 161 8141 6210 2803 3209 ", "8090 6380 3498 3014 7650 7062 8853 5939 4578 ", "8647 4020 4844 3362 4930 9447 1346 6162 8242 ", "9276 6967 589 6960 5467 8768 9018 8155 3886 ", "7274" }

    Returns: 37305252

    One hundred points.

  5. { "2 2 3 3 25 26" }

    { "2 3 2 3 26 25" }

    Returns: 9

    The optimal solution contains strictly more than half of the points (i.e. 4 of the 6 points).

  6. { "5481 3318 5721 9019 ", "1618 9762 1654 2275 ", "5361 307 6833 9456 ", "7473 6088 9685 2725" }

    { "1181 7762 3889 7015 ", " 5445 9063 2510 8229 ", " 4390 6454 9197 708 ", " 2221 9012 2665 8308" }

    Returns: 25959465

  7. { "9999 10000 9999 10000 0 0" }

    { "9999 9999 10000 10000 1 0" }

    Returns: 9

    Testing that they can handle the max coordinate (10000). Also, the optimal solution has an edge at 10001.

  8. { "3703 4215 8089 5444 8575 8771 9198 3706 1168 7817 ", "8744 9111 8230 8912 3794 2653 5789 8897 9756 298 2", "854 7345 5200 5862 4977 988 2133 3234 7202 99 1097", " 9649 2603 9317 2354 4584 2173 2197 4122 2113 4184", " 910 6327 8030 6278 9896 3663 6922 1579 5083 4896 ", "8514 842 8308 6264 7076 6307 9925 5635 2430 9328 1", "316 606 6233 3066 2984 8143 2562 3593 3191 5552 75", "82 7584 6801 2571 9055 2470 3819 2216 2848 5379 24", "47 3616 193 491 1978 3556 6439 543 6751 4690 9310 ", "7127 3550 7438 2284 6150 1353 9513 6569" }

    { "9622 9077 3445 1707 8908 9843 1251 2082 7165 2425 ", "8703 5615 9105 4492 2025 2066 4043 1627 8980 8637 ", "2374 1697 2075 2832 2465 724 2421 3560 2014 9590 7", "702 5323 6895 229 8166 7462 4814 7229 5242 225 750", " 5684 8402 2108 6050 9059 7247 8410 3302 1378 7430", " 9206 4704 6558 1000 6079 2435 3925 4023 841 5815 ", "3059 6921 6216 1441 2954 5877 7980 9375 233 6874 4", "55 504 8617 7426 2346 7694 7189 4948 7959 6042 815", "2 4826 9574 5637 5675 5718 406 3570 6232 4399 3941", " 651 7380 7554 4706 2249 6316 3305 7573" }

    Returns: 37240602

    100 random points - the numbers may split across two Strings

  9. { "20 20 20 20 21 21 22 22 23 23 23 23" }

    { "20 21 22 23 20 23 20 23 20 21 22 23" }

    Returns: 15

    These points are on the boundary of a rectangle

  10. { "8326 2368 ", "8711 1078 ", "6764 3682 ", "2815 5794 ", "5396 8601 ", "4874 8393 ", "6918 1301 ", "9654 5559 ", "2185 33 41", "99 1759 51", "72 2766 89", "45 8286 27", "30 1998 48", "17 6564 88", "43 8455 45", "75 8713 11", "84 6578 30", "64 1134 50", "73 9577 16", "25 6253 61", "81 8158 64", "34 3414 87", "39 5005 92", "13 2471 38", "2 6583 146", "0 2559 830", "2 4882 96 ", "4203 3856 ", "4386 3281 ", "5041 4489 ", "3694 16 81", "54 2397 70", "13 6142 73", "18 9174 80", "18 2300 52", "83 4442 75", "04 6595 96", "47 4349 66", "22 5725 58", "13 2706 95", "72 3663 81", "07 3583 31", "26 6161 81", "61 9165 55", "20 2708 44", "01 823 392", "1 4987 762", "8 4529 794", "9 2274 551", "6" }

    { "264 9741 1", "366 1093 9", "123 2312 5", "843 3886 8", "042 4941 5", "811 4887 2", "873 1007 1", "642 7887 6", "591 8242 8", "943 2917 7", "125 6934 2", "632 2356 6", "415 1558 8", "874 2800 8", "870 5885 6", "385 8558 6", "724 3872 4", "403 7428 4", "390 8637 5", "84 7144 38", "72 9630 84", "70 1309 84", "99 3757 77", "1 6955 283", "2 9663 175", "5 1936 247", "0 5618 918", "8 9342 861", "1 581 3981", " 7760 8802", " 4804 3526", " 839 7028 ", "1143 2924 ", "6902 3486 ", "672 6866 9", "553 6770 6", "556 3719 3", "184 8955 8", "270 2582 3", "107 7138 4", "192 3453 8", "586 3345 4", "352 524 85", "19 8388 67", "11 8618 37", "27 4280 97", "11 3245 68", "17 4097 10", "36 5442 48", "9" }

    Returns: 30819977

    Testing that they can handle 50 Strings

  11. { "1242 9594 6816 833 6587 7183 9355 7087 ", " ", "8675 5944 786 3597 1327 9884 7138 8073 ", "", "3017 5468 331 8136" }

    { "1105 7791 7865 8119 ", "9950 8261 5988 1708 ", "1615 5400 487 4837 4712 5777 3819 ", "", "5063 5143 5990 2895 4375", "" }

    Returns: 18598707

  12. { "6464 5847 507 9809 6173 5854 6846 3184 3835 5138 3", "887 4671 7403 9614 5211 5101 3800 227 3213 9540 52", "65 9401 7421 5985 5819 9436 8483 5437 2119 6428 60", "93 4384 9496 2430 9014 4507 9707 9332 9324 4667 16", "45 259 1008 7087 34 8180 5132 3055 27 6805 9933 34", "51 7538 5928 4408 5910 6104 1860 8234 3556 1166 37", "87 9151 9883 1723 8523 1406 593 7510 9438 5233 596", "5 7102 92 7901 6692 8607 9541 1459 2031 9999 4176 ", "893 1565 569 486 9179 930 8442 4197 2426 7442 1652", " 3831 9198 3712 1923 995 2914 6094" }

    { "4046 4332 7437 5388 1381 8776 380 7904 3937 2337 9", "533 4548 8112 1798 4352 8871 3156 3255 6524 3001 7", "621 7633 8061 9257 9341 8308 4460 1693 3013 9679 4", "659 7467 6758 2619 2043 6353 9216 5168 1073 5623 1", "731 4589 2251 6647 5947 9962 4060 9025 5740 2838 4", "314 7840 3853 7199 4896 9718 7801 8908 3249 3765 6", "660 9207 1201 4186 229 6369 6699 2387 4689 4602 68", "45 7731 4377 9508 1286 7745 7596 4975 3429 552 545", "5 7249 3222 4569 6681 8096 9328 3098 8046 489 384 ", "4359 9619 7036 4742 692 6389 3490 5603 4209" }

    Returns: 35258236

  13. { "3038 6124 7379 4762 954 3434 2752 1843 3297 2866 2", "950 5149 2962 3777 3522 2232 5691 3489 247 1958 50", "55 1557 7575 3977 492 2214 1117 2005 303 4432 3010", " 1406 4580 1546 661 6419 5954 4699 2211 9271 294 8", "29 8665 2960 22 2000 6619 7819 6877 1022 3871 117 ", "4940 1600 1952 3141 1055 4361 7666 2142 834 782 78", "27 5738 1976 4596 2349 428 8003 2740 142 5745 1660", " 596 7752 2870 9783 1269 4401 2601 4206 8024 191 2", "835 1622 2784 6505 728 7912 2249 5306 3649 6628 20", "18 26 2646 3720 4595 1417 2875" }

    { "6100 3185 454 1040 3700 4543 1469 2827 3698 1467 4", "983 3500 5379 2601 1692 1796 1045 3904 4261 5036 1", "638 5102 2455 2286 6607 5 8006 2420 2849 8244 1827", " 5784 4561 4306 1700 1524 5267 140 2021 3630 3230 ", "334 4639 1629 9042 4550 3828 3271 3217 4222 1656 2", "403 3246 3895 1498 252 3414 729 1423 4703 3264 826", "3 2584 305 982 4632 2108 6439 4432 1479 3346 4677 ", "1911 5218 4091 3836 2664 5058 8627 2623 4492 2101 ", "716 2787 96 542 3066 2159 1572 266 5956 6688 5515 ", "3557 6734 2213 302 376 1687 3683" }

    Returns: 17372293

    100 points that are not spread apart evenly

  14. { "0 0 10000 10000" }

    { "0 10000 0 10000" }

    Returns: 20004

    The four corners

  15. { "1 2 3 6 7 8 9 10" }

    { "2 2 2 2 2 2 2 2" }

    Returns: 10

    All of these points are on a horizontal line

  16. { "3 3 3 3 3 3 3 3 3 3"}

    { "4698 4006 5705 5663 1582 843 9272 7567 4093 9678" }

    Returns: 3402

    All of these points are on a vertical line

  17. { "6435 6613 9229 9888 302 7805 4260 5150 7", "543 1808 2973 6654 6346 6957 8812 5074 8", "441 2311 7079 8073 1101 146 6780 2805 83", "59 4171 3592 3171 2133 1855 4811 7592 25", "7 5608 1694 8941 3768 5516 3252 755 243 ", "5818 8263 2898 3437 8387 9046 5396 2057 ", "9096 1352 1391 2086 7148 9630 8820 7763 ", "3200 5882 5729 6055 9411 3338 6012 8270 ", "3437 3259 698 284 8847 4317 4969 9836 63", "79 9215 2544 5262 4115 2467 7220" }

    { "6149 9942 3080 7203 4499 5734 9123 302 8", "950 8183 9775 3355 7617 7899 341 4876 92", "30 3247 6130 1415 2898 99 8366 4478 6721", " 8494 9883 3195 5810 5049 7389 6746 969 ", "1611 5415 6093 7688 2601 8122 5466 1383 ", "5792 9108 192 8899 3832 6033 8994 8135 6", "737 6478 5657 7410 8787 3736 7104 3633 6", "780 6477 2338 3725 440 4145 9459 6806 99", "36 775 6014 5690 9897 3496 1336 4908 414", "3 8418 8154 9117 374 5831 4805" }

    Returns: 30143600

    80 random points

  18. { "5434 5387 8656 1638 2003 6850 5076 18 61", "36 4596 2011 7250 5199 3586 8471 5653 39", "3 550 9056 5686" }

    { "5434 5387 8656 1638 2003 6850 5076 18 61", "36 4596 2011 7250 5199 3586 8471 5653 39", "3 550 9056 5686" }

    Returns: 7054336

    These points are on the y=x line

  19. { "100", " 200" }

    { "100 2", "00" }

    Returns: 4

    Remember to concatenate the elements of X and Y first.

  20. {"1 2 3 4"}

    {"1 2 3 4"}

    Returns: 9

  21. { "6816 5800 3650 8830 3129 4460 3219 5586 3378 1233 ", "3140 467 1464 2028 3275 3602 7932 5832 4119 1580 3", "321 6777 4065 1467 6960 6281 4802 2944 7097 7226 6", "993 7756 4292 5698 7663 3726 5024 940 4052 5272 65", "73 862 6077 3555 7431 8684 1013 7211 9716 6144 950", "1 8917 1361 37 1597 3993 6230 1817 5198 4688 9705 ", "4470 6886 7833 5808 6977 7022 4145 9456 4258 6722 ", "4632 4039 9721 4256 3246 237 8246 2370 5244 6656 9", "825 6028 7532 6733 7850 2182 702 9176 1585 9294 24", "37 1140 9286 4537 8463 4335 7030 915 367" }

    { "934 897 8060 7908 1723 4706 872 7589 2753 6894 196", "4 7084 4769 2033 2359 7094 6520 5534 191 8946 7018", " 255 5092 9634 3106 576 3040 7729 3704 4046 9131 1", "136 5290 9043 7172 5434 5414 6642 553 5869 2326 63", "09 8388 7033 9175 7934 4593 1654 646 7255 5262 403", "1 8418 7777 1461 4182 9316 9904 404 5978 6716 7206", " 7859 6230 1381 508 8592 1979 2654 2755 9673 111 4", "749 1537 3542 6788 5734 1577 3887 4183 8709 6472 7", "579 8549 5691 7558 192 6708 4759 7907 948 7753 104", " 1116 5325 2929 2850 7857 43 9492" }

    Returns: 33935621

    100 random points

  22. { "1055 8254 459 7750 8551 1984 9576 7620 3160 7353 4", "25 6596 6149 4347 6750 8181 6255 438 5707 255 8974", " 8737 3766 8971 8193 12 3625 2568 5435 1791 6514 9", "093 9947 4555 8072 5751 4995 8501 8801 3191 1842 4", "274 2080 4927 3093 7635 3649 712 1371 1098 6571 28", "06 7604 5262 4764 5740 5604 8743 6385 3467 6075 84", "37 5555 2586 3696 1156 7261 6686 5511 3614 5585 48", "42 7509 177 9862 6747 8955 6877 6844 8068 842 5719", " 9506 2201 5623 5534 4719 8844 294 4299 2728 5495 ", "3867 3163 1053 5352 3253 4243 4301 3934" }

    { "105 6773 299 4791 52 2105 5150 8429 9631 12 7910 2", "828 4289 5111 9239 517 8711 7185 3561 1183 4510 39", "63 8512 8841 3821 7900 8317 7145 2964 8726 4939 65", "88 2196 8165 9017 4640 4679 5775 1133 105 213 5169", " 2819 5902 7047 8008 5826 294 8105 9109 7667 5190 ", "6382 9777 1218 1548 7893 8027 6230 6155 9590 3760 ", "1024 1079 3960 4150 3361 6967 1623 9506 471 3994 8", "190 2698 9601 9797 1897 5876 2066 1954 4064 6640 5", "770 3750 5311 2108 3406 5792 6651 3371 6192 2871 6", "052 4732 5819 4917 7894 1800 585 3298" }

    Returns: 36102030

    100 random points

  23. { "2343 2759 5775 3039 5251 1551 2325 8498 1799 8274 ", "2141 4928 3075 7110 4176 1677 2407 631 5331 2032 6", "260 9323 4258 4131 5742 8979 1065 8988 2804 6106 7", "345 7729 5718 817 7295 6559 3003 2644 6027 5899 36", "09 7111 5599 9625 3876 9999 2789 1435 8561 1792 51", "70 7974 4022 6968 3674 2521 6607 1503 489 8862 816", "4 7277 887 2174 3688 3864 6351 2762 3147 6644 4266", " 8793 687 5114 6348 6272 9639 6820 3947 8027 982 4", "35 3464 8598 6293 6152 9162 8630 3543 2782 3902 59", "4 5640 8755 506 7525 7047 8527 7781 7771" }

    { "6414 4557 2746 9204 3059 1386 1798 9534 8399 9329 ", "2634 2109 6785 6659 4320 4219 4106 3734 1601 3533 ", "2633 8707 2206 1262 6656 4963 6262 4881 1189 5528 ", "3168 2635 383 5026 3332 1407 4505 5530 7014 4101 4", "340 8649 209 2655 9706 2524 7968 8027 4381 9107 88", "24 9058 3235 3975 149 7993 8560 8297 3129 1603 171", "2 86 7791 3374 3059 9828 3081 3995 7872 3730 4304 ", "4553 8394 6431 441 9208 2572 3773 6800 1923 8096 5", "460 4284 4853 6351 6833 5152 4353 4622 8796 6530 4", "285 6489 5017 7225 5270 9704 5916 376 2834" }

    Returns: 32437167

    100 random points

  24. { "7456 5237 4789 3128 733 6957 3060 1231 1861 7459 8", "130 8848 2767 5902 9902 8375 3836 6351 3698 540 78", "13 5975 8617 5386 1510 6864 9024 2748 7229 2887 99", "66 9762 9512 6893 9315 6352 5809 8982 5651 9613 14", "65 3607 1058 4547 500 1795 2302 1702 3653 4926 215", "2 1910 4294 8189 5063 4561 979 5095 7812 8627 2663", " 9233 6269 4976 8859 5815 4024 4462 2441 3555 7238", " 8702 7171 6848 2805 9530 5515 9337 3677 8682 4915", " 2573 6009 1434 2216 7645 7715 6637 6691 3413 6951", " 870 1799 2322 2060 6304 4637 3593 1614 220" }

    { "995 2779 4639 1165 323 6417 5607 7553 6916 6932 26", "62 5787 7250 7567 2576 631 9431 5380 3007 2583 653", "4 9770 2102 8968 4206 8770 5707 6000 7958 792 2183", " 4443 2035 2282 2111 6287 2259 1079 6431 6284 9832", " 1210 1928 68 1714 7302 7441 150 5923 5818 7579 20", "66 6830 5945 3360 5667 6398 5099 754 662 2167 2735", " 8778 1320 1775 1461 8562 2513 6791 6239 3585 8204", " 5743 942 9126 3887 7360 6447 5926 6511 227 5998 9", "042 8949 4370 1674 7879 1265 3554 455 7571 7653 45", "43 9580 4990 6202 950 8695 4932 8479" }

    Returns: 37868765

    100 random points

  25. { "9853 8648 6237 4900 7435 3988 6865 2283 9202 3428 ", "9113 4689 9669 3168 1612 4323 5416 3733 132 4146 7", "766 2934 249 779 965 4068 1623 778 2679 101 5396 8", "286 2150 8852 9311 2112 1531 2515 4840 9405 7574 7", "297 6799 1236 4097 5316 8713 2706 504 1519 6578 63", "94 7964 2886 9516 3420 2817 5871 8346 770 6303 712", " 2080 7011 703 8027 7995 1101 4699 3931 3032 598 4", "861 4807 3069 6232 5994 1820 1817 9569 345 8270 30", "06 9265 4570 9985 7876 9292 3784 59 5007 9428 4042", " 4497 1024 4298 8144 4528 8824 2294" }

    { "7382 2272 2028 976 1725 5622 5334 8711 2745 164 53", "58 7754 2045 4135 2428 2625 8126 9623 6052 8429 37", "05 5489 7177 376 7861 7808 2579 7074 5070 8314 195", " 8612 8383 4668 8884 4575 608 3774 7341 281 5690 7", "80 4647 1788 2215 1972 9281 1513 2434 9311 4363 66", "69 3045 8018 4327 2119 8558 6329 2273 7804 4066 82", "81 7864 8353 1931 6248 2737 9193 6017 9829 4188 90", "67 7931 1634 8114 3676 1968 8559 9072 8890 9410 91", "68 8724 4899 8186 4032 3885 4560 997 5975 1955 180", " 3481 1520 4584 3056 4184 3137 92 9173" }

    Returns: 37471200

    100 random points

  26. { "66 50 56 9946 41 65 80 9911 32 9986 9961 72 42 100", "00 94 87 9963 9967 9961 9983 9910 29 9937 68 9924 ", "0 7 34 41 9985 9958 9964 9994 7 9993 9903 2 9975 9", "913 9930 49 9916 10 70 79 8 59 99 9949 68 9912 46 ", "9913 72 57 49 18 75 9923 9985 46 96 9977 24 49 91 ", "9991 85 9914 9953 9991 9995 3 9952 9925 9942 9995 ", "12 9964 66 9928 69 93 9901 9968 98 0 20 2 4 62 993", "6 93 79 76 9997 96 9904 5 9965" }

    { "71 74 23 9907 18 9977 9928 9948 12 9927 18 79 9928", " 22 39 7 72 80 9998 58 9920 9905 83 9910 30 9941 9", "904 30 65 69 9991 9993 80 9949 9983 79 53 9977 15 ", "45 31 18 9999 9932 9950 9914 9935 73 9925 40 83 99", "40 9993 9944 9944 43 9944 65 6 9909 9956 9990 9912", " 72 9958 29 9920 66 8 9986 32 9948 70 9947 53 77 9", "913 9992 18 9941 8 9914 9937 99 9985 96 9978 9906 ", "40 9952 9903 92 9939 9918 21 9921 9945 9949 9954 6", "2" }

    Returns: 909909

    100 points within 100 of the border

  27. { "196 10 27 9957 9825 170 15 188 34 194 9982 95 0 69", " 9938 24 9970 9891 95 62 155 107 9856 9914 71 78 9", "845 9880 9981 185 9963 9974 189 156 68 9982 76 981", "7 9865 9927 137 9814 9914 134 9817 175 173 9835 19", "3 9803 9958 118 9812 9813 192 9929 9992 73 72 166 ", "62 9949 138 183 9956 9844 9931 62 9834 181 25 9990", " 9927 9869 126 9893 134 9925 9844 9950 156 94 9997", " 9935 9832 183 165 9967 9910 9949 9925 92 86 7 22 ", "9850 9844 9855 12 170" }

    { "11 9823 9939 9977 164 17 121 9972 9974 9958 192 48", " 9807 9894 9935 9863 109 29 9978 80 9842 9966 194 ", "101 133 118 9823 9880 113 9899 131 9875 7 104 9888", " 9807 9848 60 9831 138 97 9972 33 68 9980 39 9815 ", "9877 9867 9853 163 169 9819 9860 9819 9861 9932 99", "46 9916 9825 130 37 9882 91 25 89 59 9992 44 9956 ", "164 9989 9908 101 57 9921 52 67 6 117 9962 83 9976", " 9870 9903 24 39 9915 9910 9995 176 9996 9882 47 7", "0 8 192 9888 9990 57" }

    Returns: 1827987

    100 points within 200 of the border

  28. {"5481 3318 5721 9019 ", "1618 9762 1654 2275 ", "5361 307 6833 9456 ", "7473 6088 9685 2725" }

    {"1181 7762 3889 7015 ", " 5445 9063 2510 8229 ", " 4390 6454 9197 708 ", " 2221 9012 2665 8308" }

    Returns: 25959465

  29. {"4496 6443 2837 557 4098 1083 3466 1250 6126 ", "3135 7598 9274 9180 5128 741 7625 8316 414 ", "9071 8753 5509 1080 2797 906 3805 698 947 ", "8645 9640 2596 6883 1845 9169 3922 4792 7919 ", "7389 9397 4901 1343 3347 6366 9118 3148 780 ", "4541 9479 483 1174 9615 8900 3067 5397 9879 ", "7440 8948 846 8881 7602 6760 3327 5197 9017 ", "5463 6781 2478 6270 5392 9420 9069 3609 6401 ", "1810 6680 6787 9840 1031 1916 5415 1168 5154 ", "2727 8834 9125 3961 4289 4750 5524 5118 5258 ", "2652 7020 9770 5866 3386 6447 7960 3889 2158 ", "6717" }

    {"6801 8243 9390 2156 5505 5509 3442 6663 1294 ", "9979 1008 5644 7516 5442 5909 4550 2431 2779 ", "419 4744 8155 7800 2944 4169 1633 1464 7353 ", "5365 1548 3073 8596 4461 2540 4664 5057 1870 ", "4782 4028 8003 9175 2592 4520 2420 6955 519 ", "2141 1580 5170 9138 4268 9724 1093 5633 9820 ", "3411 9789 6200 7661 2296 8644 8259 8631 4342 ", "574 530 6664 8812 161 8141 6210 2803 3209 ", "8090 6380 3498 3014 7650 7062 8853 5939 4578 ", "8647 4020 4844 3362 4930 9447 1346 6162 8242 ", "9276 6967 589 6960 5467 8768 9018 8155 3886 ", "7274" }

    Returns: 37305252

  30. {"4496 6443 2837 557 4098 1083 3466 1250 6126 ", "3135 7598 9274 9180 5128 741 7425 8316 414 ", "921 8753 5509 10 2797 906 3805 698 947 ", "8645 9640 2596 6883 1845 9169 4922 4792 7919 ", "79 9397 4901 1343 3347 6366 9418 3148 780 ", "4541 9479 483 1174 9615 8900 3067 5397 9879 ", "7440 8948 846 8881 7602 6760 3337 5197 9017 ", "5463 6781 2478 1111 5392 9420 9069 3609 6401 ", "1810 6680 6787 6270 1031 1916 5415 1168 5154 ", "2727 8834 9125 3961 4289 4750 5524 518 58 ", "2652 7020 9770 5861 3186 6247 7360 3189 258 ", "6717" }

    {"6801 8243 9390 2156 5505 5509 3442 6663 1294 ", "9979 1008 5644 7516 5442 5909 2150 2431 2779 ", "419 4744 8155 7800 2944 4169 1633 64 7353 ", "5365 1548 3073 8596 4461 2540 4664 5057 1870 ", "42 4028 8003 9175 2592 4520 2420 6955 5239 ", "241 1580 5170 9138 4268 9724 1093 5633 9820 ", "31 9789 6200 7661 1213 8644 8259 8631 4342 ", "574 530 6664 8812 161 8141 6210 2803 3209 ", "8090 6380 3498 3014 7650 7062 8853 5939 48 ", "8647 4020 4844 3362 4930 9447 1346 6162 8242 ", "9276 6967 589 6960 5467 8768 9018 8155 3886 ", "7274" }

    Returns: 39966720

  31. {"5481 3318 5721 9019 ", "1618 9762 1654 2275 ", "5361 307 6833 546 ", "7473 6088 9685 2725" }

    {"1181 7762 3889 7015 ", " 5445 9063 2510 8229 ", " 4390 6454 9197 708 ", " 2221 9012 2665 8308" }

    Returns: 25959465

  32. {"5481 3318 5721 9019 ", "1618 9762 1654 2275 ", "5361 307 6833 9456 ", "7473 6088 96", "85 2726" }

    {"1181 7762 3889 7015 ", " 5445 9063 2510 8229 ", " 4390 6454 9197 708 ", " 2221 9012 2665 8308" }

    Returns: 25959465

  33. {"2566 7583 3478 1296 7485 5342 9410 8505 2244 7144 ", "4488 1840 646 2885 2502 4768 9541 2515 9116 8953 4", "514 9617 1089 6044 5847 2484 30 7408 7933 8661 641", "6 8576 3430 4209 7706 7162 869 2601 545 9345 1457 ", "7088 8143 6604 2117 2879 6833 3157 9859 1540 1640 ", "9195 5324 3054 2108 977 6426 1187 2212 2253 5623 9", "274 2687 7018 3443 1634 831 4662 6721 2457 9320 81", "48 6474 4341 3142 1818 6473 7071 2132 8836 8237 54", "11 1637 6112 6731 3314 9407 9937 153 8832 9979 463", "6 2756 4822 6999 3630 59 7584 4100 5204" }

    {"7853 3268 4096 6049 5454 497 6034 7795 4866 7025 1", "578 1246 327 427 3217 7856 6572 3913 656 9662 4520", " 4952 9513 65 1268 1612 477 2949 3964 8745 1732 54", "97 6306 4843 4616 7202 3995 255 8698 871 4960 2231", " 92 2598 4078 266 1957 7118 4983 402 2080 3651 127", "9 7693 8797 9006 1007 2540 4622 9914 6054 4743 811", " 8168 7571 6327 8111 1771 811 5482 7369 1037 5977 ", "8659 8925 9000 9545 4391 7568 1870 6701 817 1823 4", "02 1929 8767 5400 9612 2406 8099 4671 3433 178 50 ", "1082 1992 4814 4536 7446 1694" }

    Returns: 36859648

  34. {"1 2 5 10000" }

    {"5 2 4 10000" }

    Returns: 15

  35. {"1", "0 2", "0 3", "0 4", "0" }

    {"1", "0 2", "0 3", "0 4", "0" }

    Returns: 144

  36. {"100 ", " 1", "0000" }

    {"100 2", "00", "0" }

    Returns: 4

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