Statistics

Problem Statement for "SetOfBoxes"

Problem Statement

You have a large square box and some smaller triangular boxes (all two-dimensional). The triangular boxes all lie inside the square box. Triangular boxes may lie inside other triangular boxes, but they must not overlap. You randomly throw an object (represented as a point) into the square box, and you want to know if it lands inside exactly inBox triangular boxes.

You are given a String[] boxes, each element of which is formatted as "X1.Y1 X2.Y2 X3.Y3" (quotes for clarity only), representing the three corners of a triangular box. The large square box has sides parallel to the axes, and has corners at (0, 0) and (100, 100). Return the probability (between 0 and 1) that a random point within the square is contained in exactly inBox triangular boxes.

Definition

Class:
SetOfBoxes
Method:
countThrow
Parameters:
String[], int
Returns:
double
Method signature:
double countThrow(String[] boxes, int inBox)
(be sure your method is public)

Notes

  • Your return value must have an absolute or relative error less than 1e-9.

Constraints

  • boxes will contain between 0 and 50 elements, inclusive.
  • Each element of boxes will be formatted as "X1.Y1 X2.Y2 X3.Y3" (quotes for clarity only).
  • X1, Y1, X2, Y2, X3, Y3 will be integers with no leading zeros, each between 0 and 100, inclusive.
  • Triangles represented by different elements of boxes will have no common points.
  • inBox will be between 0 and 50, inclusive.

Examples

  1. {"0.0 1.0 0.1"}

    1

    Returns: 5.0E-5

  2. {"0.0 20.0 0.10", "1.1 6.1 1.5"}

    1

    Returns: 0.0090

    Here it is the area of the first triangle minus the area of the second one.

  3. {"0.0 10.0 0.20", "0.100 0.90 20.100", "50.50 60.60 50.70", "51.55 55.60 51.65"}

    1

    Returns: 0.028

  4. {"0.0 10.0 0.20", "0.100 0.90 20.100", "50.50 60.60 50.70", "51.55 55.60 51.65"}

    0

    Returns: 0.97

  5. {}

    5

    Returns: 0.0

  6. {}

    0

    Returns: 1.0

  7. {"0.0 0.100 100.0", "99.100 100.100 100.99"}

    1

    Returns: 0.50005

  8. {"0.0 0.100 100.0", "99.100 100.100 100.99"}

    50

    Returns: 0.0

  9. {"0.0 0.100 100.0", "1.1 1.98 98.1", "2.2 2.96 96.2", "3.3 3.94 94.3", "4.4 4.92 92.4", "5.5 5.90 90.5", "6.6 6.88 88.6", "7.7 7.86 86.7", "8.8 8.84 84.8", "9.9 9.82 82.9", "10.10 10.80 80.10", "11.11 11.78 78.11", "12.12 12.76 76.12", "13.13 13.74 74.13", "14.14 14.72 72.14", "15.15 15.70 70.15", "16.16 16.68 68.16", "17.17 17.66 66.17", "18.18 18.64 64.18", "19.19 19.62 62.19", "20.20 20.60 60.20", "21.21 21.58 58.21", "22.22 22.56 56.22", "23.23 23.54 54.23", "24.24 24.52 52.24", "25.25 25.50 50.25", "26.26 26.48 48.26", "27.27 27.46 46.27", "28.28 28.44 44.28", "29.29 29.42 42.29", "30.30 30.40 40.30", "31.31 31.38 38.31", "32.32 32.36 36.32", "33.33 33.34 34.33"}

    0

    Returns: 0.5

  10. {"0.0 0.100 100.0", "1.1 1.98 98.1", "2.2 2.96 96.2", "3.3 3.94 94.3", "4.4 4.92 92.4", "5.5 5.90 90.5", "6.6 6.88 88.6", "7.7 7.86 86.7", "8.8 8.84 84.8", "9.9 9.82 82.9", "10.10 10.80 80.10", "11.11 11.78 78.11", "12.12 12.76 76.12", "13.13 13.74 74.13", "14.14 14.72 72.14", "15.15 15.70 70.15", "16.16 16.68 68.16", "17.17 17.66 66.17", "18.18 18.64 64.18", "19.19 19.62 62.19", "20.20 20.60 60.20", "21.21 21.58 58.21", "22.22 22.56 56.22", "23.23 23.54 54.23", "24.24 24.52 52.24", "25.25 25.50 50.25", "26.26 26.48 48.26", "27.27 27.46 46.27", "28.28 28.44 44.28", "29.29 29.42 42.29", "30.30 30.40 40.30", "31.31 31.38 38.31", "32.32 32.36 36.32", "33.33 33.34 34.33"}

    4

    Returns: 0.02685

  11. {"0.0 0.100 100.0", "1.1 1.98 98.1", "2.2 2.96 96.2", "3.3 3.94 94.3", "4.4 4.92 92.4", "5.5 5.90 90.5", "6.6 6.88 88.6", "7.7 7.86 86.7", "8.8 8.84 84.8", "9.9 9.82 82.9", "10.10 10.80 80.10", "11.11 11.78 78.11", "12.12 12.76 76.12", "13.13 13.74 74.13", "14.14 14.72 72.14", "15.15 15.70 70.15", "16.16 16.68 68.16", "17.17 17.66 66.17", "18.18 18.64 64.18", "19.19 19.62 62.19", "20.20 20.60 60.20", "21.21 21.58 58.21", "22.22 22.56 56.22", "23.23 23.54 54.23", "24.24 24.52 52.24", "25.25 25.50 50.25", "26.26 26.48 48.26", "27.27 27.46 46.27", "28.28 28.44 44.28", "29.29 29.42 42.29", "30.30 30.40 40.30", "31.31 31.38 38.31", "32.32 32.36 36.32", "33.33 33.34 34.33"}

    18

    Returns: 0.01425

  12. {"0.0 0.100 100.0", "1.1 1.98 98.1", "2.2 2.96 96.2", "3.3 3.94 94.3", "4.4 4.92 92.4", "5.5 5.90 90.5", "6.6 6.88 88.6", "7.7 7.86 86.7", "8.8 8.84 84.8", "9.9 9.82 82.9", "10.10 10.80 80.10", "11.11 11.78 78.11", "12.12 12.76 76.12", "13.13 13.74 74.13", "14.14 14.72 72.14", "15.15 15.70 70.15", "16.16 16.68 68.16", "17.17 17.66 66.17", "18.18 18.64 64.18", "19.19 19.62 62.19", "20.20 20.60 60.20", "21.21 21.58 58.21", "22.22 22.56 56.22", "23.23 23.54 54.23", "24.24 24.52 52.24", "25.25 25.50 50.25", "26.26 26.48 48.26", "27.27 27.46 46.27", "28.28 28.44 44.28", "29.29 29.42 42.29", "30.30 30.40 40.30", "31.31 31.38 38.31", "32.32 32.36 36.32", "33.33 33.34 34.33"}

    33

    Returns: 7.5E-4

  13. {"0.0 0.100 100.0", "1.1 1.98 98.1", "2.2 2.96 96.2", "3.3 3.94 94.3", "4.4 4.92 92.4", "5.5 5.90 90.5", "6.6 6.88 88.6", "7.7 7.86 86.7", "8.8 8.84 84.8", "9.9 9.82 82.9", "10.10 10.80 80.10", "11.11 11.78 78.11", "12.12 12.76 76.12", "13.13 13.74 74.13", "14.14 14.72 72.14", "15.15 15.70 70.15", "16.16 16.68 68.16", "17.17 17.66 66.17", "18.18 18.64 64.18", "19.19 19.62 62.19", "20.20 20.60 60.20", "21.21 21.58 58.21", "22.22 22.56 56.22", "23.23 23.54 54.23", "24.24 24.52 52.24", "25.25 25.50 50.25", "26.26 26.48 48.26", "27.27 27.46 46.27", "28.28 28.44 44.28", "29.29 29.42 42.29", "30.30 30.40 40.30", "31.31 31.38 38.31", "32.32 32.36 36.32", "33.33 33.34 34.33"}

    34

    Returns: 5.0E-5

  14. {"100.100 0.100 100.0", "99.99 2.99 99.2", "98.98 4.98 98.4", "97.97 6.97 97.6", "96.96 8.96 96.8", "95.95 10.95 95.10", "94.94 12.94 94.12", "93.93 14.93 93.14", "92.92 16.92 92.16", "91.91 18.91 91.18", "90.90 20.90 90.20", "89.89 22.89 89.22", "88.88 24.88 88.24", "87.87 26.87 87.26", "86.86 28.86 86.28", "85.85 30.85 85.30", "84.84 32.84 84.32", "83.83 34.83 83.34", "82.82 36.82 82.36", "81.81 38.81 81.38", "80.80 40.80 80.40", "79.79 42.79 79.42", "78.78 44.78 78.44", "77.77 46.77 77.46", "76.76 48.76 76.48", "75.75 50.75 75.50", "74.74 52.74 74.52", "73.73 54.73 73.54", "72.72 56.72 72.56", "71.71 58.71 71.58", "70.70 60.70 70.60", "69.69 62.69 69.62", "68.68 64.68 68.64", "67.67 66.67 67.66"}

    0

    Returns: 0.5

  15. {"100.100 0.100 100.0", "99.99 2.99 99.2", "98.98 4.98 98.4", "97.97 6.97 97.6", "96.96 8.96 96.8", "95.95 10.95 95.10", "94.94 12.94 94.12", "93.93 14.93 93.14", "92.92 16.92 92.16", "91.91 18.91 91.18", "90.90 20.90 90.20", "89.89 22.89 89.22", "88.88 24.88 88.24", "87.87 26.87 87.26", "86.86 28.86 86.28", "85.85 30.85 85.30", "84.84 32.84 84.32", "83.83 34.83 83.34", "82.82 36.82 82.36", "81.81 38.81 81.38", "80.80 40.80 80.40", "79.79 42.79 79.42", "78.78 44.78 78.44", "77.77 46.77 77.46", "76.76 48.76 76.48", "75.75 50.75 75.50", "74.74 52.74 74.52", "73.73 54.73 73.54", "72.72 56.72 72.56", "71.71 58.71 71.58", "70.70 60.70 70.60", "69.69 62.69 69.62", "68.68 64.68 68.64", "67.67 66.67 67.66"}

    4

    Returns: 0.02685

  16. {"100.100 0.100 100.0", "99.99 2.99 99.2", "98.98 4.98 98.4", "97.97 6.97 97.6", "96.96 8.96 96.8", "95.95 10.95 95.10", "94.94 12.94 94.12", "93.93 14.93 93.14", "92.92 16.92 92.16", "91.91 18.91 91.18", "90.90 20.90 90.20", "89.89 22.89 89.22", "88.88 24.88 88.24", "87.87 26.87 87.26", "86.86 28.86 86.28", "85.85 30.85 85.30", "84.84 32.84 84.32", "83.83 34.83 83.34", "82.82 36.82 82.36", "81.81 38.81 81.38", "80.80 40.80 80.40", "79.79 42.79 79.42", "78.78 44.78 78.44", "77.77 46.77 77.46", "76.76 48.76 76.48", "75.75 50.75 75.50", "74.74 52.74 74.52", "73.73 54.73 73.54", "72.72 56.72 72.56", "71.71 58.71 71.58", "70.70 60.70 70.60", "69.69 62.69 69.62", "68.68 64.68 68.64", "67.67 66.67 67.66"}

    18

    Returns: 0.01425

  17. {"100.100 0.100 100.0", "99.99 2.99 99.2", "98.98 4.98 98.4", "97.97 6.97 97.6", "96.96 8.96 96.8", "95.95 10.95 95.10", "94.94 12.94 94.12", "93.93 14.93 93.14", "92.92 16.92 92.16", "91.91 18.91 91.18", "90.90 20.90 90.20", "89.89 22.89 89.22", "88.88 24.88 88.24", "87.87 26.87 87.26", "86.86 28.86 86.28", "85.85 30.85 85.30", "84.84 32.84 84.32", "83.83 34.83 83.34", "82.82 36.82 82.36", "81.81 38.81 81.38", "80.80 40.80 80.40", "79.79 42.79 79.42", "78.78 44.78 78.44", "77.77 46.77 77.46", "76.76 48.76 76.48", "75.75 50.75 75.50", "74.74 52.74 74.52", "73.73 54.73 73.54", "72.72 56.72 72.56", "71.71 58.71 71.58", "70.70 60.70 70.60", "69.69 62.69 69.62", "68.68 64.68 68.64", "67.67 66.67 67.66"}

    33

    Returns: 7.5E-4

  18. {"100.100 0.100 100.0", "99.99 2.99 99.2", "98.98 4.98 98.4", "97.97 6.97 97.6", "96.96 8.96 96.8", "95.95 10.95 95.10", "94.94 12.94 94.12", "93.93 14.93 93.14", "92.92 16.92 92.16", "91.91 18.91 91.18", "90.90 20.90 90.20", "89.89 22.89 89.22", "88.88 24.88 88.24", "87.87 26.87 87.26", "86.86 28.86 86.28", "85.85 30.85 85.30", "84.84 32.84 84.32", "83.83 34.83 83.34", "82.82 36.82 82.36", "81.81 38.81 81.38", "80.80 40.80 80.40", "79.79 42.79 79.42", "78.78 44.78 78.44", "77.77 46.77 77.46", "76.76 48.76 76.48", "75.75 50.75 75.50", "74.74 52.74 74.52", "73.73 54.73 73.54", "72.72 56.72 72.56", "71.71 58.71 71.58", "70.70 60.70 70.60", "69.69 62.69 69.62", "68.68 64.68 68.64", "67.67 66.67 67.66"}

    34

    Returns: 5.0E-5

  19. {"0.0 100.0 50.100", "1.1 99.1 50.99", "2.2 98.2 50.98", "3.3 97.3 50.97", "4.4 96.4 50.96", "5.5 95.5 50.95", "6.6 94.6 50.94", "7.7 93.7 50.93", "8.8 92.8 50.92", "9.9 91.9 50.91", "10.10 90.10 50.90", "11.11 89.11 50.89", "12.12 88.12 50.88", "13.13 87.13 50.87", "14.14 86.14 50.86", "15.15 85.15 50.85", "16.16 84.16 50.84", "17.17 83.17 50.83", "18.18 82.18 50.82", "19.19 81.19 50.81", "20.20 80.20 50.80", "21.21 79.21 50.79", "22.22 78.22 50.78", "23.23 77.23 50.77", "24.24 76.24 50.76", "25.25 75.25 50.75", "26.26 74.26 50.74", "27.27 73.27 50.73", "28.28 72.28 50.72", "29.29 71.29 50.71", "30.30 70.30 50.70", "31.31 69.31 50.69", "32.32 68.32 50.68", "33.33 67.33 50.67", "34.34 66.34 50.66", "35.35 65.35 50.65", "36.36 64.36 50.64", "37.37 63.37 50.63", "38.38 62.38 50.62", "39.39 61.39 50.61", "40.40 60.40 50.60", "41.41 59.41 50.59", "42.42 58.42 50.58", "43.43 57.43 50.57", "44.44 56.44 50.56", "45.45 55.45 50.55", "46.46 54.46 50.54", "47.47 53.47 50.53", "48.48 52.48 50.52", "49.49 51.49 50.51"}

    50

    Returns: 2.0E-4

  20. {"0.0 100.0 50.100", "1.1 99.1 50.99", "2.2 98.2 50.98", "3.3 97.3 50.97", "4.4 96.4 50.96", "5.5 95.5 50.95", "6.6 94.6 50.94", "7.7 93.7 50.93", "8.8 92.8 50.92", "9.9 91.9 50.91", "10.10 90.10 50.90", "11.11 89.11 50.89", "12.12 88.12 50.88", "13.13 87.13 50.87", "14.14 86.14 50.86", "15.15 85.15 50.85", "16.16 84.16 50.84", "17.17 83.17 50.83", "18.18 82.18 50.82", "19.19 81.19 50.81", "20.20 80.20 50.80", "21.21 79.21 50.79", "22.22 78.22 50.78", "23.23 77.23 50.77", "24.24 76.24 50.76", "25.25 75.25 50.75", "26.26 74.26 50.74", "27.27 73.27 50.73", "28.28 72.28 50.72", "29.29 71.29 50.71", "30.30 70.30 50.70", "31.31 69.31 50.69", "32.32 68.32 50.68", "33.33 67.33 50.67", "34.34 66.34 50.66", "35.35 65.35 50.65", "36.36 64.36 50.64", "37.37 63.37 50.63", "38.38 62.38 50.62", "39.39 61.39 50.61", "40.40 60.40 50.60", "41.41 59.41 50.59", "42.42 58.42 50.58", "43.43 57.43 50.57", "44.44 56.44 50.56", "45.45 55.45 50.55", "46.46 54.46 50.54", "47.47 53.47 50.53", "48.48 52.48 50.52", "49.49 51.49 50.51"}

    49

    Returns: 6.0E-4

  21. {"0.0 100.0 50.100", "1.1 99.1 50.99", "2.2 98.2 50.98", "3.3 97.3 50.97", "4.4 96.4 50.96", "5.5 95.5 50.95", "6.6 94.6 50.94", "7.7 93.7 50.93", "8.8 92.8 50.92", "9.9 91.9 50.91", "10.10 90.10 50.90", "11.11 89.11 50.89", "12.12 88.12 50.88", "13.13 87.13 50.87", "14.14 86.14 50.86", "15.15 85.15 50.85", "16.16 84.16 50.84", "17.17 83.17 50.83", "18.18 82.18 50.82", "19.19 81.19 50.81", "20.20 80.20 50.80", "21.21 79.21 50.79", "22.22 78.22 50.78", "23.23 77.23 50.77", "24.24 76.24 50.76", "25.25 75.25 50.75", "26.26 74.26 50.74", "27.27 73.27 50.73", "28.28 72.28 50.72", "29.29 71.29 50.71", "30.30 70.30 50.70", "31.31 69.31 50.69", "32.32 68.32 50.68", "33.33 67.33 50.67", "34.34 66.34 50.66", "35.35 65.35 50.65", "36.36 64.36 50.64", "37.37 63.37 50.63", "38.38 62.38 50.62", "39.39 61.39 50.61", "40.40 60.40 50.60", "41.41 59.41 50.59", "42.42 58.42 50.58", "43.43 57.43 50.57", "44.44 56.44 50.56", "45.45 55.45 50.55", "46.46 54.46 50.54", "47.47 53.47 50.53", "48.48 52.48 50.52", "49.49 51.49 50.51"}

    48

    Returns: 0.0010

  22. {"0.0 100.0 50.100", "1.1 99.1 50.99", "2.2 98.2 50.98", "3.3 97.3 50.97", "4.4 96.4 50.96", "5.5 95.5 50.95", "6.6 94.6 50.94", "7.7 93.7 50.93", "8.8 92.8 50.92", "9.9 91.9 50.91", "10.10 90.10 50.90", "11.11 89.11 50.89", "12.12 88.12 50.88", "13.13 87.13 50.87", "14.14 86.14 50.86", "15.15 85.15 50.85", "16.16 84.16 50.84", "17.17 83.17 50.83", "18.18 82.18 50.82", "19.19 81.19 50.81", "20.20 80.20 50.80", "21.21 79.21 50.79", "22.22 78.22 50.78", "23.23 77.23 50.77", "24.24 76.24 50.76", "25.25 75.25 50.75", "26.26 74.26 50.74", "27.27 73.27 50.73", "28.28 72.28 50.72", "29.29 71.29 50.71", "30.30 70.30 50.70", "31.31 69.31 50.69", "32.32 68.32 50.68", "33.33 67.33 50.67", "34.34 66.34 50.66", "35.35 65.35 50.65", "36.36 64.36 50.64", "37.37 63.37 50.63", "38.38 62.38 50.62", "39.39 61.39 50.61", "40.40 60.40 50.60", "41.41 59.41 50.59", "42.42 58.42 50.58", "43.43 57.43 50.57", "44.44 56.44 50.56", "45.45 55.45 50.55", "46.46 54.46 50.54", "47.47 53.47 50.53", "48.48 52.48 50.52", "49.49 51.49 50.51"}

    0

    Returns: 0.5

  23. {"0.0 100.0 50.100", "1.1 99.1 50.99", "2.2 98.2 50.98", "3.3 97.3 50.97", "5.5 95.5 50.95", "6.6 94.6 50.94", "7.7 93.7 50.93", "8.8 92.8 50.92", "9.9 91.9 50.91", "10.10 90.10 50.90", "11.11 89.11 50.89", "12.12 88.12 50.88", "13.13 87.13 50.87", "14.14 86.14 50.86", "15.15 85.15 50.85", "16.16 84.16 50.84", "17.17 83.17 50.83", "18.18 82.18 50.82", "19.19 81.19 50.81", "20.20 80.20 50.80", "21.21 79.21 50.79", "22.22 78.22 50.78", "23.23 77.23 50.77", "24.24 76.24 50.76", "25.25 75.25 50.75", "26.26 74.26 50.74", "27.27 73.27 50.73", "28.28 72.28 50.72", "29.29 71.29 50.71", "30.30 70.30 50.70", "31.31 69.31 50.69", "32.32 68.32 50.68", "33.33 67.33 50.67", "35.35 65.35 50.65", "36.36 64.36 50.64", "38.38 62.38 50.62", "39.39 61.39 50.61", "40.40 60.40 50.60", "41.41 59.41 50.59", "42.42 58.42 50.58", "43.43 57.43 50.57", "44.44 56.44 50.56", "45.45 55.45 50.55", "46.46 54.46 50.54", "47.47 53.47 50.53", "48.48 52.48 50.52", "49.49 51.49 50.51"}

    8

    Returns: 0.0166

  24. {"1.1 99.1 50.99", "2.2 98.2 50.98", "6.6 94.6 50.94", "7.7 93.7 50.93", "10.10 90.10 50.90", "11.11 89.11 50.89", "12.12 88.12 50.88", "13.13 87.13 50.87", "15.15 85.15 50.85", "16.16 84.16 50.84", "17.17 83.17 50.83", "18.18 82.18 50.82", "20.20 80.20 50.80", "21.21 79.21 50.79", "22.22 78.22 50.78", "24.24 76.24 50.76", "25.25 75.25 50.75", "26.26 74.26 50.74", "27.27 73.27 50.73", "28.28 72.28 50.72", "31.31 69.31 50.69", "32.32 68.32 50.68", "33.33 67.33 50.67", "34.34 66.34 50.66", "35.35 65.35 50.65", "36.36 64.36 50.64", "37.37 63.37 50.63", "38.38 62.38 50.62", "40.40 60.40 50.60", "42.42 58.42 50.58", "43.43 57.43 50.57", "47.47 53.47 50.53", "49.49 51.49 50.51"}

    21

    Returns: 0.0074

  25. {"0.0 100.0 50.100", "5.5 95.5 50.95", "8.8 92.8 50.92", "10.10 90.10 50.90", "13.13 87.13 50.87", "14.14 86.14 50.86", "17.17 83.17 50.83", "19.19 81.19 50.81", "21.21 79.21 50.79", "22.22 78.22 50.78", "28.28 72.28 50.72", "29.29 71.29 50.71", "30.30 70.30 50.70", "31.31 69.31 50.69", "32.32 68.32 50.68", "35.35 65.35 50.65", "37.37 63.37 50.63", "42.42 58.42 50.58", "43.43 57.43 50.57", "48.48 52.48 50.52", "49.49 51.49 50.51"}

    4

    Returns: 0.0462

  26. {"3.3 97.3 50.97", "6.6 94.6 50.94", "7.7 93.7 50.93", "10.10 90.10 50.90", "17.17 83.17 50.83", "19.19 81.19 50.81", "20.20 80.20 50.80", "23.23 77.23 50.77", "25.25 75.25 50.75", "30.30 70.30 50.70", "36.36 64.36 50.64", "45.45 55.45 50.55", "46.46 54.46 50.54", "49.49 51.49 50.51"}

    10

    Returns: 0.0408

  27. {"0.0 99.0 0.99", "100.0 100.100 0.100", "1.1 50.25 1.50", "60.1 80.1 70.5", "65.2 67.2 66.3", "3.3 4.4 3.4", "7.7 8.8 7.8" }

    2

    Returns: 0.12385

  28. { }

    0

    Returns: 1.0

  29. {"0.0 1.0 0.1" }

    1

    Returns: 5.0E-5

  30. {"0.0 0.100 100.0", "1.1 41.1 1.41", "3.3 12.3 5.17", "6.5 10.5 5.8", "15.2 37.2 8.29", "17.3 31.3 16.19", "12.22 12.23 13.22", "21.5 19.7 23.7" }

    3

    Returns: 0.02415

  31. {"30.30 40.30 30.40", "29.29 42.29 29.42", "28.28 44.28 28.44", "27.27 46.27 27.46", "26.26 48.26 26.48", "25.25 50.25 25.50", "24.24 52.24 24.52", "23.23 54.23 23.54", "22.22 56.22 22.56", "21.21 58.21 21.58", "20.20 60.20 20.60", "19.19 62.19 19.62", "18.18 64.18 18.64", "17.17 66.17 17.66", "16.16 68.16 16.68", "15.15 70.15 15.70", "14.14 72.14 14.72", "13.13 74.13 13.74", "12.12 76.12 12.76", "11.11 78.11 11.78", "10.10 80.10 10.80", "9.9 82.9 9.82", "8.8 84.8 8.84", "7.7 86.7 7.86", "6.6 88.6 6.88", "5.5 90.5 5.90", "4.4 92.4 4.92", "3.3 94.3 3.94", "2.2 96.2 2.96", "1.1 98.1 1.98", "28.94 34.68 97.76", "66.52 74.30 54.67", "99.100 61.91 76.85", "68.67 96.22 84.57", "79.85 100.80 92.86", "96.18 78.46 78.36", "89.52 89.71 82.63", "77.75 43.77 41.90", "55.85 76.81 75.76", "96.7 99.9 100.61", "93.10 93.20 72.40", "70.45 66.60 70.46", "10.93 39.95 2.99", "98.2 76.24 62.42", "92.67 95.74 94.53", "100.95 83.89 73.83", "51.99 45.90 72.98", "96.58 92.47 98.62", "93.40 88.51 92.39", "25.88 19.81 19.83" }

    0

    Returns: 0.3293

  32. {"30.30 40.30 30.40", "29.29 42.29 29.42", "28.28 44.28 28.44", "27.27 46.27 27.46", "26.26 48.26 26.48", "25.25 50.25 25.50", "24.24 52.24 24.52", "23.23 54.23 23.54", "22.22 56.22 22.56", "21.21 58.21 21.58", "20.20 60.20 20.60", "19.19 62.19 19.62", "18.18 64.18 18.64", "17.17 66.17 17.66", "16.16 68.16 16.68", "15.15 70.15 15.70", "14.14 72.14 14.72", "13.13 74.13 13.74", "12.12 76.12 12.76", "11.11 78.11 11.78", "10.10 80.10 10.80", "9.9 82.9 9.82", "8.8 84.8 8.84", "7.7 86.7 7.86", "6.6 88.6 6.88", "5.5 90.5 5.90", "4.4 92.4 4.92", "3.3 94.3 3.94", "2.2 96.2 2.96", "1.1 98.1 1.98", "28.94 34.68 97.76", "66.52 74.30 54.67", "99.100 61.91 76.85", "68.67 96.22 84.57", "79.85 100.80 92.86", "96.18 78.46 78.36", "89.52 89.71 82.63", "77.75 43.77 41.90", "55.85 76.81 75.76", "96.7 99.9 100.61", "93.10 93.20 72.40", "70.45 66.60 70.46", "10.93 39.95 2.99", "98.2 76.24 62.42", "92.67 95.74 94.53", "100.95 83.89 73.83", "51.99 45.90 72.98", "96.58 92.47 98.62", "93.40 88.51 92.39", "25.88 19.81 19.83" }

    2

    Returns: 0.0551

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