LINGO的TSP的实现

最短路径LINGO源代码：
MODEL:
SETS:
CITY / 1.. 33/: U; ! U( I) = sequence no. of city;
LINK( CITY, CITY):
DIST, ! The distance matrix;
X; ! X( I, J) = 1 if we use link I, J;
ENDSETS
DATA: !Distance matrix, it need not be symmetric;
DIST =
0.0 127.4 1208.5 1770.0 292.2 507.0 691.5 989.2 1244.3 1238.2
1300.1 1034.4 1887.4 1424.3 422.1 683.1 1157.0 1427.3 2113.2 2693.4 1804.7 2152.5 2653.0 1094.6 1486.2 1690.1 3638.2 2320.8 487.4 1141.7 2956.6 2200.8 2252.6
127.4 0.0 1086.9 1794.4 304.8 534.4 665.6 970.6 1225.7 881.4 1150.3 937.6 1765.9 1311.2 325.3 654.7 1072.2 1454.2 2095.1 2675.2 1829.2 2070.2 3634.9 1119.0 1468.2 1664.8 3579.5 2273.9 599.2 1205.6 3196.1 2111.6 2234.5
1208.5 1086.9 0.0 1708.4 1096.1 1346.5 1734.8 2039.9 2295.0 296.1 173.7 456.4 765.7 732.7 840.8 955.5 840.0 1088.3 1402.7 2029.8 1069.0 1846.1 2346.6 1386.9 2035.1 2274.7 4222.8 1887.5 1596.4 1596.1 3921.3 1514.2 1585.5
1770.0 1794.4 1708.4 0.0 1470.0 1283.0 2429.8 2734.8 2989.9 1396.4 1605.9 1241.4 1774.9 1212.2 1545.2 1140.9 868.4 893.0 1313.7 1428.5 311.7 372.1 880.2 683.0 981.1 1191.1 2395.7 923.4 1645.3 1433.2 2876.7 1472.6 1441.5
292.2 304.8 1096.1 1470.0 0.0 240.8 966.8 1271.8 1526.9 914.7 1176.6 910.9 1790.7 1164.7 298.6 406.2 887.7 1203.7 1936.6 2424.8 1521.1 1883.9 2384.4 811.0 1243.3 1447.2 3395.3 2054.4 503.9 935.4 2925.9 1933.8 1964.5
507.0 534.4 1346.5 1283.0 240.8 0.0 1185.9 1490.9 1746.0 1077.7 1341.5 1004.6 1847.4 1284.8 526.7 432.5 937.7 1220.7 1861.5 2441.7 1318.7 1657.5 2163.2 608.6 1048.3 1252.2 3200.4 2082.1 436.6 740.5 2730.9 2024.0 2000.9
691.5 665.6 1734.8 2429.8 966.8 1185.9 0.0 380.4 585.6 1547.0 1798.7 1594.4 2414.3 2005.8 982.1 1362.6 1795.6 2111.0 2751.9 3332.0 2478.7 2791.2 3291.7 1768.6 2163.0 2366.9 4315.1 2972.4 1164.7 1855.2 3845.7 2839.5 2891.2
989.2 970.6 2039.9 2734.8 1271.8 1490.9 380.4 0.0 258.1 1839.4 2091.0 1886.8 2706.6 2298.2 1274.5 1655.0 2088.0 2403.4 3044.3 3624.4 2771.1 3083.5 3584.0 2061.0 2351.9 2548.5 4463.2 3264.8 1334.0 2064.1 3812.1 3131.8 3183.6
1244.3 1225.7 2295.0 2989.9 1526.9 1746.0 585.6 258.1 0.0 2107.2 2358.8 2154.6 2974.4 2565.9 1542.2 1922.7 2355.7 2671.1 3312.0
3892.1 3038.8 3351.3 3851.8 2328.7 2723.1 2927.1 4875.2 3532.5
1517.7 2331.8 3987.0 3399.6 3451.4
1238.2 881.4 296.1 1396.4 914.7 1077.7 1547.0 1839.4 2107.2 0.0 276.7 163.6 910.8 579.3 636.8 665.7 535.2 869.9 1356.7
1954.2 1680.4 1638.9 2148.1 1100.2 1722.5 1958.7 3907.7 1744.9
1502.9 1698.9 3615.3 1436.0 1513.4
1300.1 1150.3 173.7 1605.9 1176.6 1341.5 1798.7 2091.0 2358.8 276.7
0.0 408.4 634.0 547.3 901.5 934.7 724.6 907.8 1276.6 1853.6
1858.2 1665.0 2174.1 1367.0 1989.3 2175.0 4121.0 1720.5 1758.4
1945.8 3828.6 1335.3 1412.7
1034.4 937.6 456.4 1241.4 910.9 1004.6 1594.4 1886.8 2154.6 163.6 408.4 0.0 943.5 434.5 626.9 570.6 379.6 724.0 1210.8 1787.8 1514.1 1483.3 1992.4 911.5 1540.1 1776.3 3725.2 1599.0 1441.0
1601.6 3432.8 1269.5 1346.9
1887.4 1765.9 765.7 1774.9 1790.7 1847.4 2414.3 2706.6 2974.4 910.8 634.0 943.5 0.0 569.9 1518.4 1421.9 917.9 901.3 865.0 1444.3 2051.5 1585.6 2094.7 1644.4 2272.9 2509.1 4458.1 1423.4 2292.4
2369.5 4165.7 858.1 973.1
1424.3 1311.2 732.7 1212.2 1164.7 1284.8 2005.8 2298.2 2565.9 579.3 547.3 434.5 569.9 0.0 1053.8 857.5 353.5 339.2 781.6 1358.5 1487.1 1144.7 1653.8 1080.0 1708.5 1944.7 3893.7 1200.2 1728.0
1805.1 3601.3 840.3 945.3
422.1 325.3 840.8 1545.2 298.6 526.7 982.1 1274.5 1542.2 636.8 901.5 626.9 1518.4 1053.8 0.0 436.9 843.1 1166.7 1815.0 2391.9 1603.7 1846.2 2355.3 892.5 1445.5 1646.1 5395.1 2041.7 915.2
1224.5 3125.1 1882.1 1957.4
683.1 654.7 955.5 1140.9 406.2 432.5 1362.6 1655.0 1922.7 665.7 934.7 570.6 1421.9 857.5 436.9 0.0 539.0 800.4 1448.6 2025.6 1188.7 1479.9 1989.0 477.5 1099.8 1336.0 3284.9 1675.4 876.8
1037.3 2992.6 1611.4 1591.0
1157.0 1072.2 840.0 868.4 887.7 937.7 1795.6 2088.0 2355.7 535.2 724.6 379.6 917.9 353.5 843.1 539.0 0.0 345.5 985.9 1566.5 1143.1 1087.2 1618.8 731.4 1382.6 1622.2 3219.5 1203.7 1376.9
1365.0 3223.2 1089.9 1113.8
1427.3 1454.2 1088.3 893.0 1203.7 1220.7 2111.0 2403.4 2671.1 869.9 907.8 724.0 901.3 339.2 1166.7 800.4 345.5 0.0 661.8 1280.9 1194.8 837.3 1337.8 950.7 1633.2 1872.8 3230.2 869.0 1614.6
1584.3 3442.5 806.4 789.7
2113.2 2095.1 1402.7 1313.7 1936.6 1861.5 2751.9 3044.3 3312.0 1356.7 1276.6 1210.8 865.0 781.6 1815.0 1448.6 985.9 661.8 0.0 590.5 1658.9 992.3 1326.0 1593.3 2279.8 2519.4 3535.0 556.6 2257.2
2226.9 4085.1 163.3 131.6
2693.4 2675.2 2029.8 1428.5 2424.8 2441.7 3332.0 3624.4 3892.1 1954.2 1853.6 1787.8 1444.3 1358.5 2391.9 2025.6 1566.5 1280.9 590.5 0.0
1710.8 1060.6 1226.7 2107.5 2407.3 2618.1 3435.7 474.0 2878.4
2855.1 4302.8 641.9 573.5
1804.7 1829.2 1069.0 311.7 1521.1 1318.7 2478.7 2771.1 3038.8 1680.4 1858.2 1514.1 2051.5 1487.1 1603.7 1188.7 1143.1 1194.8 1658.9
1710.8 0.0 676.2 899.9 712.9 854.3 964.3 2088.8 1242.7 1685.6 1434.6 2696.7 1821.7 1791.7
2152.5 2070.2 1846.1 372.1 1883.9 1657.5 2791.2 3083.5 3351.3 1638.9 1665.0 1483.3 1585.6 1144.7 1846.2 1479.9 1087.2 837.3 992.3
1060.6 676.2 0.0 507.5 1050.5 1355.0 1565.8 2648.3 558.9 2012.8 1802.8 3250.6 1150.1 1098.3
2653.0 3634.9 2346.6 880.2 2384.4 2163.2 3291.7 3584.0 3851.8 2148.1 2174.1 1992.4 2094.7 1653.8 2355.3 1989.0 1618.8 1337.8 1326.0
1226.7 899.9 507.5 0.0 1562.2 1765.8 1976.7 2213.1 770.6 2544.1 2309.8 3661.4 1541.0 1402.4
1094.6 1119.0 1386.9 683.0 811.0 608.6 1768.6 2061.0 2328.7 1100.2 1367.0 911.5 1644.4 1080.0 892.5 477.5 731.4 950.7 1593.3
2107.5 712.9 1050.5 1562.2 0.0 646.0 885.5 2833.7 1602.7 963.6 634.8 2493.1 1736.4 1719.6
1486.2 1468.2 2035.1 981.1 1243.3 1048.3 2163.0 2351.9 2723.1 1722.5 1989.3 1540.1 2272.9 1708.5 1445.5 1099.8 1382.6 1633.2 2279.8
2407.3 854.3 1355.0 1765.8 646.0 0.0 215.1 2129.8 1921.7 1112.4 430.0 1903.1 2439.3 2416.2
1690.1 1664.8 2274.7 1191.1 1447.2 1252.2 2366.9 2548.5 2927.1 1958.7 2175.0 1776.3 2509.1 1944.7 1646.1 1336.0 1622.2 1872.8 2519.4
2618.1 964.3 1565.8 1976.7 885.5 215.1 0.0 1915.6 2129.0 1312.7 605.7 1734.4 2677.2 2654.1
3638.2 3579.5 4222.8 2395.7 3395.3 3200.4 4315.1 4463.2 4875.2 3907.7 4121.0 3725.2 4458.1 3893.7 5395.1 3284.9 3219.5 3230.2 3535.0
3435.7 2088.8 2648.3 2213.1 2833.7 2129.8 1915.6 0.0 2979.2 3263.6 2519.0 2646.5 3760.5 3611.0
2320.8 2273.9 1887.5 923.4 2054.4 2082.1 2972.4 3264.8 3532.5 1744.9 1720.5 1599.0 1423.4 1200.2 2041.7 1675.4 1203.7 869.0 556.6
474.0 1242.7 558.9 770.6 1602.7 1921.7 2129.0 2979.2 0.0 2522.3 2367.3 3815.1 720.5 632.6
487.4 599.2 1596.4 1645.3 503.9 436.6 1164.7 1334.0 1517.7 1502.9 1758.4 1441.0 2292.4 1728.0 915.2 876.8 1376.9 1614.6 2257.2
2878.4 1685.6 2012.8 2544.1 963.6 1112.4 1312.7 3263.6 2522.3 0.0 635.0 2479.3 2462.0 2438.9
1141.7 1205.6 1596.1 1433.2 935.4 740.5 1855.2 2064.1 2331.8 1698.9 1945.8 1601.6 2369.5 1805.1 1224.5 1037.3 1365.0 1584.3 2226.9
2855.1 1434.6 1802.8 2309.8 634.8 430.0 605.7 2519.0 2367.3
635.0 0.0 2078.4 2370.7 2354.0
2956.6 3196.1 3921.3 2876.7 2925.9 2730.9 3845.7 3812.1 3987.0 3615.3 3828.6 3432.8 4165.7 3601.3 3125.1 2992.6 3223.2 3442.5 4085.1
4302.8 2696.7 3250.6 3661.4 2493.1 1903.1 1734.4 2646.5 3815.1
2479.3 2078.4 0.0 4227.9 4221.2
2200.8 2111.6 1514.2 1472.6 1933.8 2024.0 2839.5 3131.8 3399.6 1436.0 1335.3 1269.5 858.1 840.3 1882.1 1611.4 1089.9 806.4 163.3
641.9 1821.7 1150.1 1541.0 1736.4 2439.3 2677.2 3760.5 720.5
2462.0 2370.7 4227.9 0.0 72.5
2252.6 2234.5 1585.5 1441.5 1964.5 2000.9 2891.2 3183.6 3451.4 1513.4 1412.7 1346.9 973.1 945.3 1957.4 1591.0 1113.8 789.7 131.6
573.5 1791.7 1098.3 1402.4 1719.6 2416.2 2654.1 3611.0 632.6
2438.9 2354.0 4221.2 72.5 0.0
;
ENDDATA
!The model:Ref. Desrochers & Laporte, OR Letters, Feb. 91;
N = @SIZE( CITY);
MIN = @SUM( LINK: DIST * X);
@FOR( CITY( K):
! It must be entered;
@SUM( CITY( I)| I #NE# K: X( I, K)) = 1;
! It must be departed;
@SUM( CITY( J)| J #NE# K: X( K, J)) = 1;
! Weak form of the subtour breaking constraints;
! These are not very powerful for large problems;
@FOR( CITY( J)| J #GT# 1 #AND# J #NE# K:
U( J) >= U( K) + X ( K, J) -
( N - 2) * ( 1 - X( K, J)) +
( N - 3) * X( J, K)));
! Make the X's 0/1;
@FOR( LINK: @BIN( X));
! For the first and last stop we know...;
@FOR( CITY( K)| K #GT# 1:
U( K) <= N - 1 - ( N - 2) * X( 1, K);
U( K) >= 1 + ( N - 2) * X( K, 1));
END
结果如下：
Global optimal solution found.
Objective value: 19652.10
Objective bound: 19652.10
Infeasibilities: 0.1894781E-14
Extended solver steps: 33863
Total solver iterations: 2189844
Variable Value
N 33.00000 U( 1) 0.000000 U( 2) 4.000000 U( 3) 11.00000 U( 4) 23.00000 U( 5) 32.00000 U( 6) 31.00000 U( 7) 3.000000 U( 8) 1.000000 U( 9) 2.000000 U( 10) 10.00000 U( 11) 12.00000 U( 12) 9.000000 U( 13) 13.00000 U( 14) 14.00000 U( 15) 5.000000 U( 16) 6.000000 U( 17) 8.000000 U( 18) 15.00000 U( 19) 16.00000 U( 20) 19.00000 U( 21) 24.00000 U( 22) 22.00000 U( 23) 21.00000 U( 24) 7.000000 U( 25) 28.00000 U( 26) 27.00000 U( 27) 25.00000 U( 28) 20.00000 U( 29) 30.00000 U( 30) 29.00000 U( 31) 26.00000 U( 32) 17.00000 U( 33) 18.00000 DIST( 1, 1) 0.000000 DIST( 1, 2) 127.4000 DIST( 1, 3) 1208.500 DIST( 1, 4) 1770.000 DIST( 1, 5) 292.2000 DIST( 1, 6) 507.0000 DIST( 1, 7) 691.5000 DIST( 1, 8) 989.2000 DIST( 1, 9) 1244.300 DIST( 1, 10) 1238.200
DIST( 1, 12) 1034.400 DIST( 1, 13) 1887.400 DIST( 1, 14) 1424.300 DIST( 1, 15) 422.1000 DIST( 1, 16) 683.1000 DIST( 1, 17) 1157.000 DIST( 1, 18) 1427.300 DIST( 1, 19) 2113.200 DIST( 1, 20) 2693.400 DIST( 1, 21) 1804.700 DIST( 1, 22) 2152.500 DIST( 1, 23) 2653.000 DIST( 1, 24) 1094.600 DIST( 1, 25) 1486.200 DIST( 1, 26) 1690.100 DIST( 1, 27) 3638.200 DIST( 1, 28) 2320.800 DIST( 1, 29) 487.4000 DIST( 1, 30) 1141.700 DIST( 1, 31) 2956.600 DIST( 1, 32) 2200.800 DIST( 1, 33) 2252.600 DIST( 2, 1) 127.4000 DIST( 2, 2) 0.000000 DIST( 2, 3) 1086.900 DIST( 2, 4) 1794.400 DIST( 2, 5) 304.8000 DIST( 2, 6) 534.4000 DIST( 2, 7) 665.6000 DIST( 2, 8) 970.6000 DIST( 2, 9) 1225.700 DIST( 2, 10) 881.4000 DIST( 2, 11) 1150.300 DIST( 2, 12) 937.6000 DIST( 2, 13) 1765.900 DIST( 2, 14) 1311.200 DIST( 2, 15) 325.3000 DIST( 2, 16) 654.7000 DIST( 2, 17) 1072.200 DIST( 2, 18) 1454.200 DIST( 2, 19) 2095.100 DIST( 2, 20) 2675.200 DIST( 2, 21) 1829.200
DIST( 2, 23) 3634.900 DIST( 2, 24) 1119.000 DIST( 2, 25) 1468.200 DIST( 2, 26) 1664.800 DIST( 2, 27) 3579.500 DIST( 2, 28) 2273.900 DIST( 2, 29) 599.2000 DIST( 2, 30) 1205.600 DIST( 2, 31) 3196.100 DIST( 2, 32) 2111.600 DIST( 2, 33) 2234.500 DIST( 3, 1) 1208.500 DIST( 3, 2) 1086.900 DIST( 3, 3) 0.000000 DIST( 3, 4) 1708.400 DIST( 3, 5) 1096.100 DIST( 3, 6) 1346.500 DIST( 3, 7) 1734.800 DIST( 3, 8) 2039.900 DIST( 3, 9) 2295.000 DIST( 3, 10) 296.1000 DIST( 3, 11) 173.7000 DIST( 3, 12) 456.4000 DIST( 3, 13) 765.7000 DIST( 3, 14) 732.7000 DIST( 3, 15) 840.8000 DIST( 3, 16) 955.5000 DIST( 3, 17) 840.0000 DIST( 3, 18) 1088.300 DIST( 3, 19) 1402.700 DIST( 3, 20) 2029.800 DIST( 3, 21) 1069.000 DIST( 3, 22) 1846.100 DIST( 3, 23) 2346.600 DIST( 3, 24) 1386.900 DIST( 3, 25) 2035.100 DIST( 3, 26) 2274.700 DIST( 3, 27) 4222.800 DIST( 3, 28) 1887.500 DIST( 3, 29) 1596.400 DIST( 3, 30) 1596.100 DIST( 3, 31) 3921.300 DIST( 3, 32) 1514.200
DIST( 4, 1) 1770.000 DIST( 4, 2) 1794.400 DIST( 4, 3) 1708.400 DIST( 4, 4) 0.000000 DIST( 4, 5) 1470.000 DIST( 4, 6) 1283.000 DIST( 4, 7) 2429.800 DIST( 4, 8) 2734.800 DIST( 4, 9) 2989.900 DIST( 4, 10) 1396.400 DIST( 4, 11) 1605.900 DIST( 4, 12) 1241.400 DIST( 4, 13) 1774.900 DIST( 4, 14) 1212.200 DIST( 4, 15) 1545.200 DIST( 4, 16) 1140.900 DIST( 4, 17) 868.4000 DIST( 4, 18) 893.0000 DIST( 4, 19) 1313.700 DIST( 4, 20) 1428.500 DIST( 4, 21) 311.7000 DIST( 4, 22) 372.1000 DIST( 4, 23) 880.2000 DIST( 4, 24) 683.0000 DIST( 4, 25) 981.1000 DIST( 4, 26) 1191.100 DIST( 4, 27) 2395.700 DIST( 4, 28) 923.4000 DIST( 4, 29) 1645.300 DIST( 4, 30) 1433.200 DIST( 4, 31) 2876.700 DIST( 4, 32) 1472.600 DIST( 4, 33) 1441.500 DIST( 5, 1) 292.2000 DIST( 5, 2) 304.8000 DIST( 5, 3) 1096.100 DIST( 5, 4) 1470.000 DIST( 5, 5) 0.000000 DIST( 5, 6) 240.8000 DIST( 5, 7) 966.8000 DIST( 5, 8) 1271.800 DIST( 5, 9) 1526.900 DIST( 5, 10) 914.7000
DIST( 5, 12) 910.9000 DIST( 5, 13) 1790.700 DIST( 5, 14) 1164.700 DIST( 5, 15) 298.6000 DIST( 5, 16) 406.2000 DIST( 5, 17) 887.7000 DIST( 5, 18) 1203.700 DIST( 5, 19) 1936.600 DIST( 5, 20) 2424.800 DIST( 5, 21) 1521.100 DIST( 5, 22) 1883.900 DIST( 5, 23) 2384.400 DIST( 5, 24) 811.0000 DIST( 5, 25) 1243.300 DIST( 5, 26) 1447.200 DIST( 5, 27) 3395.300 DIST( 5, 28) 2054.400 DIST( 5, 29) 503.9000 DIST( 5, 30) 935.4000 DIST( 5, 31) 2925.900 DIST( 5, 32) 1933.800 DIST( 5, 33) 1964.500 DIST( 6, 1) 507.0000 DIST( 6, 2) 534.4000 DIST( 6, 3) 1346.500 DIST( 6, 4) 1283.000 DIST( 6, 5) 240.8000 DIST( 6, 6) 0.000000 DIST( 6, 7) 1185.900 DIST( 6, 8) 1490.900 DIST( 6, 9) 1746.000 DIST( 6, 10) 1077.700 DIST( 6, 11) 1341.500 DIST( 6, 12) 1004.600 DIST( 6, 13) 1847.400 DIST( 6, 14) 1284.800 DIST( 6, 15) 526.7000 DIST( 6, 16) 432.5000 DIST( 6, 17) 937.7000 DIST( 6, 18) 1220.700 DIST( 6, 19) 1861.500 DIST( 6, 20) 2441.700 DIST( 6, 21) 1318.700
DIST( 6, 23) 2163.200 DIST( 6, 24) 608.6000 DIST( 6, 25) 1048.300 DIST( 6, 26) 1252.200 DIST( 6, 27) 3200.400 DIST( 6, 28) 2082.100 DIST( 6, 29) 436.6000 DIST( 6, 30) 740.5000 DIST( 6, 31) 2730.900 DIST( 6, 32) 2024.000 DIST( 6, 33) 2000.900 DIST( 7, 1) 691.5000 DIST( 7, 2) 665.6000 DIST( 7, 3) 1734.800 DIST( 7, 4) 2429.800 DIST( 7, 5) 966.8000 DIST( 7, 6) 1185.900 DIST( 7, 7) 0.000000 DIST( 7, 8) 380.4000 DIST( 7, 9) 585.6000 DIST( 7, 10) 1547.000 DIST( 7, 11) 1798.700 DIST( 7, 12) 1594.400 DIST( 7, 13) 2414.300 DIST( 7, 14) 2005.800 DIST( 7, 15) 982.1000 DIST( 7, 16) 1362.600 DIST( 7, 17) 1795.600 DIST( 7, 18) 2111.000 DIST( 7, 19) 2751.900 DIST( 7, 20) 3332.000 DIST( 7, 21) 2478.700 DIST( 7, 22) 2791.200 DIST( 7, 23) 3291.700 DIST( 7, 24) 1768.600 DIST( 7, 25) 2163.000 DIST( 7, 26) 2366.900 DIST( 7, 27) 4315.100 DIST( 7, 28) 2972.400 DIST( 7, 29) 1164.700 DIST( 7, 30) 1855.200 DIST( 7, 31) 3845.700 DIST( 7, 32) 2839.500
DIST( 8, 1) 989.2000 DIST( 8, 2) 970.6000 DIST( 8, 3) 2039.900 DIST( 8, 4) 2734.800 DIST( 8, 5) 1271.800 DIST( 8, 6) 1490.900 DIST( 8, 7) 380.4000 DIST( 8, 8) 0.000000 DIST( 8, 9) 258.1000 DIST( 8, 10) 1839.400 DIST( 8, 11) 2091.000 DIST( 8, 12) 1886.800 DIST( 8, 13) 2706.600 DIST( 8, 14) 2298.200 DIST( 8, 15) 1274.500 DIST( 8, 16) 1655.000 DIST( 8, 17) 2088.000 DIST( 8, 18) 2403.400 DIST( 8, 19) 3044.300 DIST( 8, 20) 3624.400 DIST( 8, 21) 2771.100 DIST( 8, 22) 3083.500 DIST( 8, 23) 3584.000 DIST( 8, 24) 2061.000 DIST( 8, 25) 2351.900 DIST( 8, 26) 2548.500 DIST( 8, 27) 4463.200 DIST( 8, 28) 3264.800 DIST( 8, 29) 1334.000 DIST( 8, 30) 2064.100 DIST( 8, 31) 3812.100 DIST( 8, 32) 3131.800 DIST( 8, 33) 3183.600 DIST( 9, 1) 1244.300 DIST( 9, 2) 1225.700 DIST( 9, 3) 2295.000 DIST( 9, 4) 2989.900 DIST( 9, 5) 1526.900 DIST( 9, 6) 1746.000 DIST( 9, 7) 585.6000 DIST( 9, 8) 258.1000 DIST( 9, 9) 0.000000 DIST( 9, 10) 2107.200
DIST( 9, 12) 2154.600 DIST( 9, 13) 2974.400 DIST( 9, 14) 2565.900 DIST( 9, 15) 1542.200 DIST( 9, 16) 1922.700 DIST( 9, 17) 2355.700 DIST( 9, 18) 2671.100 DIST( 9, 19) 3312.000 DIST( 9, 20) 3892.100 DIST( 9, 21) 3038.800 DIST( 9, 22) 3351.300 DIST( 9, 23) 3851.800 DIST( 9, 24) 2328.700 DIST( 9, 25) 2723.100 DIST( 9, 26) 2927.100 DIST( 9, 27) 4875.200 DIST( 9, 28) 3532.500 DIST( 9, 29) 1517.700 DIST( 9, 30) 2331.800 DIST( 9, 31) 3987.000 DIST( 9, 32) 3399.600 DIST( 9, 33) 3451.400 DIST( 10, 1) 1238.200 DIST( 10, 2) 881.4000 DIST( 10, 3) 296.1000 DIST( 10, 4) 1396.400 DIST( 10, 5) 914.7000 DIST( 10, 6) 1077.700 DIST( 10, 7) 1547.000 DIST( 10, 8) 1839.400 DIST( 10, 9) 2107.200 DIST( 10, 10) 0.000000 DIST( 10, 11) 276.7000 DIST( 10, 12) 163.6000 DIST( 10, 13) 910.8000 DIST( 10, 14) 579.3000 DIST( 10, 15) 636.8000 DIST( 10, 16) 665.7000 DIST( 10, 17) 535.2000 DIST( 10, 18) 869.9000 DIST( 10, 19) 1356.700 DIST( 10, 20) 1954.200 DIST( 10, 21) 1680.400
DIST( 10, 23) 2148.100 DIST( 10, 24) 1100.200 DIST( 10, 25) 1722.500 DIST( 10, 26) 1958.700 DIST( 10, 27) 3907.700 DIST( 10, 28) 1744.900 DIST( 10, 29) 1502.900 DIST( 10, 30) 1698.900 DIST( 10, 31) 3615.300 DIST( 10, 32) 1436.000 DIST( 10, 33) 1513.400 DIST( 11, 1) 1300.100 DIST( 11, 2) 1150.300 DIST( 11, 3) 173.7000 DIST( 11, 4) 1605.900 DIST( 11, 5) 1176.600 DIST( 11, 6) 1341.500 DIST( 11, 7) 1798.700 DIST( 11, 8) 2091.000 DIST( 11, 9) 2358.800 DIST( 11, 10) 276.7000 DIST( 11, 11) 0.000000 DIST( 11, 12) 408.4000 DIST( 11, 13) 634.0000 DIST( 11, 14) 547.3000 DIST( 11, 15) 901.5000 DIST( 11, 16) 934.7000 DIST( 11, 17) 724.6000 DIST( 11, 18) 907.8000 DIST( 11, 19) 1276.600 DIST( 11, 20) 1853.600 DIST( 11, 21) 1858.200 DIST( 11, 22) 1665.000 DIST( 11, 23) 2174.100 DIST( 11, 24) 1367.000 DIST( 11, 25) 1989.300 DIST( 11, 26) 2175.000 DIST( 11, 27) 4121.000 DIST( 11, 28) 1720.500 DIST( 11, 29) 1758.400 DIST( 11, 30) 1945.800 DIST( 11, 31) 3828.600 DIST( 11, 32) 1335.300
DIST( 12, 1) 1034.400 DIST( 12, 2) 937.6000 DIST( 12, 3) 456.4000 DIST( 12, 4) 1241.400 DIST( 12, 5) 910.9000 DIST( 12, 6) 1004.600 DIST( 12, 7) 1594.400 DIST( 12, 8) 1886.800 DIST( 12, 9) 2154.600 DIST( 12, 10) 163.6000 DIST( 12, 11) 408.4000 DIST( 12, 12) 0.000000 DIST( 12, 13) 943.5000 DIST( 12, 14) 434.5000 DIST( 12, 15) 626.9000 DIST( 12, 16) 570.6000 DIST( 12, 17) 379.6000 DIST( 12, 18) 724.0000 DIST( 12, 19) 1210.800 DIST( 12, 20) 1787.800 DIST( 12, 21) 1514.100 DIST( 12, 22) 1483.300 DIST( 12, 23) 1992.400 DIST( 12, 24) 911.5000 DIST( 12, 25) 1540.100 DIST( 12, 26) 1776.300 DIST( 12, 27) 3725.200 DIST( 12, 28) 1599.000 DIST( 12, 29) 1441.000 DIST( 12, 30) 1601.600 DIST( 12, 31) 3432.800 DIST( 12, 32) 1269.500 DIST( 12, 33) 1346.900 DIST( 13, 1) 1887.400 DIST( 13, 2) 1765.900 DIST( 13, 3) 765.7000 DIST( 13, 4) 1774.900 DIST( 13, 5) 1790.700 DIST( 13, 6) 1847.400 DIST( 13, 7) 2414.300 DIST( 13, 8) 2706.600 DIST( 13, 9) 2974.400 DIST( 13, 10) 910.8000
DIST( 13, 12) 943.5000 DIST( 13, 13) 0.000000 DIST( 13, 14) 569.9000 DIST( 13, 15) 1518.400 DIST( 13, 16) 1421.900 DIST( 13, 17) 917.9000 DIST( 13, 18) 901.3000 DIST( 13, 19) 865.0000 DIST( 13, 20) 1444.300 DIST( 13, 21) 2051.500 DIST( 13, 22) 1585.600 DIST( 13, 23) 2094.700 DIST( 13, 24) 1644.400 DIST( 13, 25) 2272.900 DIST( 13, 26) 2509.100 DIST( 13, 27) 4458.100 DIST( 13, 28) 1423.400 DIST( 13, 29) 2292.400 DIST( 13, 30) 2369.500 DIST( 13, 31) 4165.700 DIST( 13, 32) 858.1000 DIST( 13, 33) 973.1000 DIST( 14, 1) 1424.300 DIST( 14, 2) 1311.200 DIST( 14, 3) 732.7000 DIST( 14, 4) 1212.200 DIST( 14, 5) 1164.700 DIST( 14, 6) 1284.800 DIST( 14, 7) 2005.800 DIST( 14, 8) 2298.200 DIST( 14, 9) 2565.900 DIST( 14, 10) 579.3000 DIST( 14, 11) 547.3000 DIST( 14, 12) 434.5000 DIST( 14, 13) 569.9000 DIST( 14, 14) 0.000000 DIST( 14, 15) 1053.800 DIST( 14, 16) 857.5000 DIST( 14, 17) 353.5000 DIST( 14, 18) 339.2000 DIST( 14, 19) 781.6000 DIST( 14, 20) 1358.500 DIST( 14, 21) 1487.100
DIST( 14, 23) 1653.800 DIST( 14, 24) 1080.000 DIST( 14, 25) 1708.500 DIST( 14, 26) 1944.700 DIST( 14, 27) 3893.700 DIST( 14, 28) 1200.200 DIST( 14, 29) 1728.000 DIST( 14, 30) 1805.100 DIST( 14, 31) 3601.300 DIST( 14, 32) 840.3000 DIST( 14, 33) 945.3000 DIST( 15, 1) 422.1000 DIST( 15, 2) 325.3000 DIST( 15, 3) 840.8000 DIST( 15, 4) 1545.200 DIST( 15, 5) 298.6000 DIST( 15, 6) 526.7000 DIST( 15, 7) 982.1000 DIST( 15, 8) 1274.500 DIST( 15, 9) 1542.200 DIST( 15, 10) 636.8000 DIST( 15, 11) 901.5000 DIST( 15, 12) 626.9000 DIST( 15, 13) 1518.400 DIST( 15, 14) 1053.800 DIST( 15, 15) 0.000000 DIST( 15, 16) 436.9000 DIST( 15, 17) 843.1000 DIST( 15, 18) 1166.700 DIST( 15, 19) 1815.000 DIST( 15, 20) 2391.900 DIST( 15, 21) 1603.700 DIST( 15, 22) 1846.200 DIST( 15, 23) 2355.300 DIST( 15, 24) 892.5000 DIST( 15, 25) 1445.500 DIST( 15, 26) 1646.100 DIST( 15, 27) 5395.100 DIST( 15, 28) 2041.700 DIST( 15, 29) 915.2000 DIST( 15, 30) 1224.500 DIST( 15, 31) 3125.100 DIST( 15, 32) 1882.100
DIST( 16, 1) 683.1000 DIST( 16, 2) 654.7000 DIST( 16, 3) 955.5000 DIST( 16, 4) 1140.900 DIST( 16, 5) 406.2000 DIST( 16, 6) 432.5000 DIST( 16, 7) 1362.600 DIST( 16, 8) 1655.000 DIST( 16, 9) 1922.700 DIST( 16, 10) 665.7000 DIST( 16, 11) 934.7000 DIST( 16, 12) 570.6000 DIST( 16, 13) 1421.900 DIST( 16, 14) 857.5000 DIST( 16, 15) 436.9000 DIST( 16, 16) 0.000000 DIST( 16, 17) 539.0000 DIST( 16, 18) 800.4000 DIST( 16, 19) 1448.600 DIST( 16, 20) 2025.600 DIST( 16, 21) 1188.700 DIST( 16, 22) 1479.900 DIST( 16, 23) 1989.000 DIST( 16, 24) 477.5000 DIST( 16, 25) 1099.800 DIST( 16, 26) 1336.000 DIST( 16, 27) 3284.900 DIST( 16, 28) 1675.400 DIST( 16, 29) 876.8000 DIST( 16, 30) 1037.300 DIST( 16, 31) 2992.600 DIST( 16, 32) 1611.400 DIST( 16, 33) 1591.000 DIST( 17, 1) 1157.000 DIST( 17, 2) 1072.200 DIST( 17, 3) 840.0000 DIST( 17, 4) 868.4000 DIST( 17, 5) 887.7000 DIST( 17, 6) 937.7000 DIST( 17, 7) 1795.600 DIST( 17, 8) 2088.000 DIST( 17, 9) 2355.700 DIST( 17, 10) 535.2000
DIST( 17, 12) 379.6000 DIST( 17, 13) 917.9000 DIST( 17, 14) 353.5000 DIST( 17, 15) 843.1000 DIST( 17, 16) 539.0000 DIST( 17, 17) 0.000000 DIST( 17, 18) 345.5000 DIST( 17, 19) 985.9000 DIST( 17, 20) 1566.500 DIST( 17, 21) 1143.100 DIST( 17, 22) 1087.200 DIST( 17, 23) 1618.800 DIST( 17, 24) 731.4000 DIST( 17, 25) 1382.600 DIST( 17, 26) 1622.200 DIST( 17, 27) 3219.500 DIST( 17, 28) 1203.700 DIST( 17, 29) 1376.900 DIST( 17, 30) 1365.000 DIST( 17, 31) 3223.200 DIST( 17, 32) 1089.900 DIST( 17, 33) 1113.800 DIST( 18, 1) 1427.300 DIST( 18, 2) 1454.200 DIST( 18, 3) 1088.300 DIST( 18, 4) 893.0000 DIST( 18, 5) 1203.700 DIST( 18, 6) 1220.700 DIST( 18, 7) 2111.000 DIST( 18, 8) 2403.400 DIST( 18, 9) 2671.100 DIST( 18, 10) 869.9000 DIST( 18, 11) 907.8000 DIST( 18, 12) 724.0000 DIST( 18, 13) 901.3000 DIST( 18, 14) 339.2000 DIST( 18, 15) 1166.700 DIST( 18, 16) 800.4000 DIST( 18, 17) 345.5000 DIST( 18, 18) 0.000000 DIST( 18, 19) 661.8000 DIST( 18, 20) 1280.900 DIST( 18, 21) 1194.800
DIST( 18, 23) 1337.800 DIST( 18, 24) 950.7000 DIST( 18, 25) 1633.200 DIST( 18, 26) 1872.800 DIST( 18, 27) 3230.200 DIST( 18, 28) 869.0000 DIST( 18, 29) 1614.600 DIST( 18, 30) 1584.300 DIST( 18, 31) 3442.500 DIST( 18, 32) 806.4000 DIST( 18, 33) 789.7000 DIST( 19, 1) 2113.200 DIST( 19, 2) 2095.100 DIST( 19, 3) 1402.700 DIST( 19, 4) 1313.700 DIST( 19, 5) 1936.600 DIST( 19, 6) 1861.500 DIST( 19, 7) 2751.900 DIST( 19, 8) 3044.300 DIST( 19, 9) 3312.000 DIST( 19, 10) 1356.700 DIST( 19, 11) 1276.600 DIST( 19, 12) 1210.800 DIST( 19, 13) 865.0000 DIST( 19, 14) 781.6000 DIST( 19, 15) 1815.000 DIST( 19, 16) 1448.600 DIST( 19, 17) 985.9000 DIST( 19, 18) 661.8000 DIST( 19, 19) 0.000000 DIST( 19, 20) 590.5000 DIST( 19, 21) 1658.900 DIST( 19, 22) 992.3000 DIST( 19, 23) 1326.000 DIST( 19, 24) 1593.300 DIST( 19, 25) 2279.800 DIST( 19, 26) 2519.400 DIST( 19, 27) 3535.000 DIST( 19, 28) 556.6000 DIST( 19, 29) 2257.200 DIST( 19, 30) 2226.900 DIST( 19, 31) 4085.100 DIST( 19, 32) 163.3000
DIST( 20, 1) 2693.400 DIST( 20, 2) 2675.200 DIST( 20, 3) 2029.800 DIST( 20, 4) 1428.500 DIST( 20, 5) 2424.800 DIST( 20, 6) 2441.700 DIST( 20, 7) 3332.000 DIST( 20, 8) 3624.400 DIST( 20, 9) 3892.100 DIST( 20, 10) 1954.200 DIST( 20, 11) 1853.600 DIST( 20, 12) 1787.800 DIST( 20, 13) 1444.300 DIST( 20, 14) 1358.500 DIST( 20, 15) 2391.900 DIST( 20, 16) 2025.600 DIST( 20, 17) 1566.500 DIST( 20, 18) 1280.900 DIST( 20, 19) 590.5000 DIST( 20, 20) 0.000000 DIST( 20, 21) 1710.800 DIST( 20, 22) 1060.600 DIST( 20, 23) 1226.700 DIST( 20, 24) 2107.500 DIST( 20, 25) 2407.300 DIST( 20, 26) 2618.100 DIST( 20, 27) 3435.700 DIST( 20, 28) 474.0000 DIST( 20, 29) 2878.400 DIST( 20, 30) 2855.100 DIST( 20, 31) 4302.800 DIST( 20, 32) 641.9000 DIST( 20, 33) 573.5000 DIST( 21, 1) 1804.700 DIST( 21, 2) 1829.200 DIST( 21, 3) 1069.000 DIST( 21, 4) 311.7000 DIST( 21, 5) 1521.100 DIST( 21, 6) 1318.700 DIST( 21, 7) 2478.700 DIST( 21, 8) 2771.100 DIST( 21, 9) 3038.800 DIST( 21, 10) 1680.400
DIST( 21, 12) 1514.100 DIST( 21, 13) 2051.500 DIST( 21, 14) 1487.100 DIST( 21, 15) 1603.700 DIST( 21, 16) 1188.700 DIST( 21, 17) 1143.100 DIST( 21, 18) 1194.800 DIST( 21, 19) 1658.900 DIST( 21, 20) 1710.800 DIST( 21, 21) 0.000000 DIST( 21, 22) 676.2000 DIST( 21, 23) 899.9000 DIST( 21, 24) 712.9000 DIST( 21, 25) 854.3000 DIST( 21, 26) 964.3000 DIST( 21, 27) 2088.800 DIST( 21, 28) 1242.700 DIST( 21, 29) 1685.600 DIST( 21, 30) 1434.600 DIST( 21, 31) 2696.700 DIST( 21, 32) 1821.700 DIST( 21, 33) 1791.700 DIST( 22, 1) 2152.500 DIST( 22, 2) 2070.200 DIST( 22, 3) 1846.100 DIST( 22, 4) 372.1000 DIST( 22, 5) 1883.900 DIST( 22, 6) 1657.500 DIST( 22, 7) 2791.200 DIST( 22, 8) 3083.500 DIST( 22, 9) 3351.300 DIST( 22, 10) 1638.900 DIST( 22, 11) 1665.000 DIST( 22, 12) 1483.300 DIST( 22, 13) 1585.600 DIST( 22, 14) 1144.700 DIST( 22, 15) 1846.200 DIST( 22, 16) 1479.900 DIST( 22, 17) 1087.200 DIST( 22, 18) 837.3000 DIST( 22, 19) 992.3000 DIST( 22, 20) 1060.600 DIST( 22, 21) 676.2000
DIST( 22, 23) 507.5000 DIST( 22, 24) 1050.500 DIST( 22, 25) 1355.000 DIST( 22, 26) 1565.800 DIST( 22, 27) 2648.300 DIST( 22, 28) 558.9000 DIST( 22, 29) 2012.800 DIST( 22, 30) 1802.800 DIST( 22, 31) 3250.600 DIST( 22, 32) 1150.100 DIST( 22, 33) 1098.300 DIST( 23, 1) 2653.000 DIST( 23, 2) 3634.900 DIST( 23, 3) 2346.600 DIST( 23, 4) 880.2000 DIST( 23, 5) 2384.400 DIST( 23, 6) 2163.200 DIST( 23, 7) 3291.700 DIST( 23, 8) 3584.000 DIST( 23, 9) 3851.800 DIST( 23, 10) 2148.100 DIST( 23, 11) 2174.100 DIST( 23, 12) 1992.400 DIST( 23, 13) 2094.700 DIST( 23, 14) 1653.800 DIST( 23, 15) 2355.300 DIST( 23, 16) 1989.000 DIST( 23, 17) 1618.800 DIST( 23, 18) 1337.800 DIST( 23, 19) 1326.000 DIST( 23, 20) 1226.700 DIST( 23, 21) 899.9000 DIST( 23, 22) 507.5000 DIST( 23, 23) 0.000000 DIST( 23, 24) 1562.200 DIST( 23, 25) 1765.800 DIST( 23, 26) 1976.700 DIST( 23, 27) 2213.100 DIST( 23, 28) 770.6000 DIST( 23, 29) 2544.100 DIST( 23, 30) 2309.800 DIST( 23, 31) 3661.400 DIST( 23, 32) 1541.000
DIST( 24, 1) 1094.600 DIST( 24, 2) 1119.000 DIST( 24, 3) 1386.900 DIST( 24, 4) 683.0000 DIST( 24, 5) 811.0000 DIST( 24, 6) 608.6000 DIST( 24, 7) 1768.600 DIST( 24, 8) 2061.000 DIST( 24, 9) 2328.700 DIST( 24, 10) 1100.200 DIST( 24, 11) 1367.000 DIST( 24, 12) 911.5000 DIST( 24, 13) 1644.400 DIST( 24, 14) 1080.000 DIST( 24, 15) 892.5000 DIST( 24, 16) 477.5000 DIST( 24, 17) 731.4000 DIST( 24, 18) 950.7000 DIST( 24, 19) 1593.300 DIST( 24, 20) 2107.500 DIST( 24, 21) 712.9000 DIST( 24, 22) 1050.500 DIST( 24, 23) 1562.200 DIST( 24, 24) 0.000000 DIST( 24, 25) 646.0000 DIST( 24, 26) 885.5000 DIST( 24, 27) 2833.700 DIST( 24, 28) 1602.700 DIST( 24, 29) 963.6000 DIST( 24, 30) 634.8000 DIST( 24, 31) 2493.100 DIST( 24, 32) 1736.400 DIST( 24, 33) 1719.600 DIST( 25, 1) 1486.200 DIST( 25, 2) 1468.200 DIST( 25, 3) 2035.100 DIST( 25, 4) 981.1000 DIST( 25, 5) 1243.300 DIST( 25, 6) 1048.300 DIST( 25, 7) 2163.000 DIST( 25, 8) 2351.900 DIST( 25, 9) 2723.100 DIST( 25, 10) 1722.500
DIST( 25, 12) 1540.100 DIST( 25, 13) 2272.900 DIST( 25, 14) 1708.500 DIST( 25, 15) 1445.500 DIST( 25, 16) 1099.800 DIST( 25, 17) 1382.600 DIST( 25, 18) 1633.200 DIST( 25, 19) 2279.800 DIST( 25, 20) 2407.300 DIST( 25, 21) 854.3000 DIST( 25, 22) 1355.000 DIST( 25, 23) 1765.800 DIST( 25, 24) 646.0000 DIST( 25, 25) 0.000000 DIST( 25, 26) 215.1000 DIST( 25, 27) 2129.800 DIST( 25, 28) 1921.700 DIST( 25, 29) 1112.400 DIST( 25, 30) 430.0000 DIST( 25, 31) 1903.100 DIST( 25, 32) 2439.300 DIST( 25, 33) 2416.200 DIST( 26, 1) 1690.100 DIST( 26, 2) 1664.800 DIST( 26, 3) 2274.700 DIST( 26, 4) 1191.100 DIST( 26, 5) 1447.200 DIST( 26, 6) 1252.200 DIST( 26, 7) 2366.900 DIST( 26, 8) 2548.500 DIST( 26, 9) 2927.100 DIST( 26, 10) 1958.700 DIST( 26, 11) 2175.000 DIST( 26, 12) 1776.300 DIST( 26, 13) 2509.100 DIST( 26, 14) 1944.700 DIST( 26, 15) 1646.100 DIST( 26, 16) 1336.000 DIST( 26, 17) 1622.200 DIST( 26, 18) 1872.800 DIST( 26, 19) 2519.400 DIST( 26, 20) 2618.100 DIST( 26, 21) 964.3000
DIST( 26, 23) 1976.700 DIST( 26, 24) 885.5000 DIST( 26, 25) 215.1000 DIST( 26, 26) 0.000000 DIST( 26, 27) 1915.600 DIST( 26, 28) 2129.000 DIST( 26, 29) 1312.700 DIST( 26, 30) 605.7000 DIST( 26, 31) 1734.400 DIST( 26, 32) 2677.200 DIST( 26, 33) 2654.100 DIST( 27, 1) 3638.200 DIST( 27, 2) 3579.500 DIST( 27, 3) 4222.800 DIST( 27, 4) 2395.700 DIST( 27, 5) 3395.300 DIST( 27, 6) 3200.400 DIST( 27, 7) 4315.100 DIST( 27, 8) 4463.200 DIST( 27, 9) 4875.200 DIST( 27, 10) 3907.700 DIST( 27, 11) 4121.000 DIST( 27, 12) 3725.200 DIST( 27, 13) 4458.100 DIST( 27, 14) 3893.700 DIST( 27, 15) 5395.100 DIST( 27, 16) 3284.900 DIST( 27, 17) 3219.500 DIST( 27, 18) 3230.200 DIST( 27, 19) 3535.000 DIST( 27, 20) 3435.700 DIST( 27, 21) 2088.800 DIST( 27, 22) 2648.300 DIST( 27, 23) 2213.100 DIST( 27, 24) 2833.700 DIST( 27, 25) 2129.800 DIST( 27, 26) 1915.600 DIST( 27, 27) 0.000000 DIST( 27, 28) 2979.200 DIST( 27, 29) 3263.600 DIST( 27, 30) 2519.000 DIST( 27, 31) 2646.500 DIST( 27, 32) 3760.500。