{"problem":{"name":"Filling 3x3 array","description":{"content":"You are given six integers: $h_1, h_2, h_3, w_1, w_2$, and $w_3$.   Consider writing a **positive** integer on each square of a $3 \\times 3$ grid so that all of the following conditions are satisfied:","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc256_c"},"statements":[{"statement_type":"Markdown","content":"You are given six integers: $h_1, h_2, h_3, w_1, w_2$, and $w_3$.  \nConsider writing a **positive** integer on each square of a $3 \\times 3$ grid so that all of the following conditions are satisfied:\n\n*   For $i=1,2,3$, the sum of numbers written in the $i$\\-th row from the top is $h_i$.\n*   For $j=1,2,3$, the sum of numbers written in the $j$\\-th column from the left is $w_i$.\n\nFor example, if $(h_1, h_2, h_3) = (5, 13, 10)$ and $(w_1, w_2, w_3) = (6, 13, 9)$, then all of the following three ways satisfy the conditions. (There are other ways to satisfy the conditions.)\n![image](https://img.atcoder.jp/ghi/42e99457e52ca5e6d335b2dbda72d9ab.png)\nHow many ways are there to write numbers to satisfy the conditions?\n\n## Constraints\n\n*   $3 \\leq h_1, h_2, h_3, w_1, w_2, w_3 \\leq 30$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$h_1$ $h_2$ $h_3$ $w_1$ $w_2$ $w_3$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc256_c","tags":[],"sample_group":[["3 4 6 3 3 7","1\n\nThe following is the only way to satisfy the conditions. Thus, $1$ should be printed.\n![image](https://img.atcoder.jp/ghi/d53ea47321716fe799854c72b7beff3c.jpg)"],["3 4 5 6 7 8","0\n\nThere may not be a way to satisfy the conditions."],["5 13 10 6 13 9","120"],["20 25 30 22 29 24","30613"]],"created_at":"2026-03-03 11:01:14"}}