{"problem":{"name":"Good Distance","description":{"content":"There are $N$ points in a $D$\\-dimensional space. The coordinates of the $i$\\-th point are $(X_{i1}, X_{i2}, ..., X_{iD})$. The distance between two points with coordinates $(y_1, y_2, ..., y_D)$ and ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc133_b"},"statements":[{"statement_type":"Markdown","content":"There are $N$ points in a $D$\\-dimensional space.\nThe coordinates of the $i$\\-th point are $(X_{i1}, X_{i2}, ..., X_{iD})$.\nThe distance between two points with coordinates $(y_1, y_2, ..., y_D)$ and $(z_1, z_2, ..., z_D)$ is $\\sqrt{(y_1 - z_1)^2 + (y_2 - z_2)^2 + ... + (y_D - z_D)^2}$.\nHow many pairs $(i, j)$ $(i < j)$ are there such that the distance between the $i$\\-th point and the $j$\\-th point is an integer?\n\n## Constraints\n\n*   All values in input are integers.\n*   $2 \\leq N \\leq 10$\n*   $1 \\leq D \\leq 10$\n*   $-20 \\leq X_{ij} \\leq 20$\n*   No two given points have the same coordinates. That is, if $i \\neq j$, there exists $k$ such that $X_{ik} \\neq X_{jk}$.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $D$\n$X_{11}$ $X_{12}$ $...$ $X_{1D}$\n$X_{21}$ $X_{22}$ $...$ $X_{2D}$\n$\\vdots$\n$X_{N1}$ $X_{N2}$ $...$ $X_{ND}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc133_b","tags":[],"sample_group":[["3 2\n1 2\n5 5\n-2 8","1\n\nThe number of pairs with an integer distance is one, as follows:\n\n*   The distance between the first point and the second point is $\\sqrt{|1-5|^2 + |2-5|^2} = 5$, which is an integer.\n*   The distance between the second point and the third point is $\\sqrt{|5-(-2)|^2 + |5-8|^2} = \\sqrt{58}$, which is not an integer.\n*   The distance between the third point and the first point is $\\sqrt{|-2-1|^2+|8-2|^2} = 3\\sqrt{5}$, which is not an integer."],["3 4\n-3 7 8 2\n-12 1 10 2\n-2 8 9 3","2"],["5 1\n1\n2\n3\n4\n5","10"]],"created_at":"2026-03-03 11:01:14"}}