{"problem":{"name":"KEYENCE building","description":{"content":"There are $N$ people numbered $1$ to $N$. Person $i$ guessed the building area of KEYENCE headquarters building to be $S_i$ square meters. The shape of KEYENCE headquarters building is shown below, wh","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc227_b"},"statements":[{"statement_type":"Markdown","content":"There are $N$ people numbered $1$ to $N$.\nPerson $i$ guessed the building area of KEYENCE headquarters building to be $S_i$ square meters.\nThe shape of KEYENCE headquarters building is shown below, where $a$ and $b$ are some **positive integers**.  \nThat is, the building area of the building can be represented as $4ab+3a+3b$.\nBased on just this information, how many of the $N$ people are guaranteed to be wrong in their guesses?\n![image](https://img.atcoder.jp/ghi/5a025c1ae6042fc146b4404219ffc176.png)\n\n## Constraints\n\n*   $1 \\leq N \\leq 20$\n*   $1 \\leq S_i \\leq 1000$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$S_1$ $\\ldots$ $S_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc227_b","tags":[],"sample_group":[["3\n10 20 39","1\n\nThe area would be $10$ square meters if $a=1,b=1$, and $39$ square meters if $a=2,b=3$.\nHowever, no pair of positive integers $a$ and $b$ would make the area $20$ square meters.\nThus, we can only be sure that Person $2$ guessed wrong."],["5\n666 777 888 777 666","3"]],"created_at":"2026-03-03 11:01:14"}}