{"problem":{"name":"Preparing Boxes","description":{"content":"There are $N$ empty boxes arranged in a row from left to right. The integer $i$ is written on the $i$\\-th box from the left $(1 \\leq i \\leq N)$. For each of these boxes, Snuke can choose either to put","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc134_d"},"statements":[{"statement_type":"Markdown","content":"There are $N$ empty boxes arranged in a row from left to right. The integer $i$ is written on the $i$\\-th box from the left $(1 \\leq i \\leq N)$.\nFor each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.\nWe say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:\n\n*   For every integer $i$ between $1$ and $N$ (inclusive), the total number of balls contained in the boxes with multiples of $i$ written on them is congruent to $a_i$ modulo $2$.\n\nDoes there exist a good set of choices? If the answer is yes, find one good set of choices.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $a_i$ is $0$ or $1$.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $...$ $a_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc134_d","tags":[],"sample_group":[["3\n1 0 0","1\n1\n\nConsider putting a ball only in the box with $1$ written on it.\n\n*   There are three boxes with multiples of $1$ written on them: the boxes with $1$, $2$, and $3$. The total number of balls contained in these boxes is $1$.\n*   There is only one box with a multiple of $2$ written on it: the box with $2$. The total number of balls contained in these boxes is $0$.\n*   There is only one box with a multiple of $3$ written on it: the box with $3$. The total number of balls contained in these boxes is $0$.\n\nThus, the condition is satisfied, so this set of choices is good."],["5\n0 0 0 0 0","0\n\nPutting nothing in the boxes can be a good set of choices."]],"created_at":"2026-03-03 11:01:14"}}