{"problem":{"name":"mod M","description":{"content":"You are given a sequence $A = (A_1, A_2, ..., A_N)$.   You may perform the following operation exactly once. *   Choose an integer $M$ at least $2$. Then, for every integer $i$ ($1 \\leq i \\leq N$), r","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc148_a"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence $A = (A_1, A_2, ..., A_N)$.  \nYou may perform the following operation exactly once.\n\n*   Choose an integer $M$ at least $2$. Then, for every integer $i$ ($1 \\leq i \\leq N$), replace $A_i$ with the remainder when $A_i$ is divided by $M$.\n\nFor instance, if $M = 4$ is chosen when $A = (2, 7, 4)$, $A$ becomes $(2 \\bmod 4, 7 \\bmod 4, 4 \\bmod 4) = (2, 3, 0)$.\nFind the minimum possible number of different elements in $A$ after the operation.\n\n## Constraints\n\n*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $0 \\leq A_i \\leq 10^9$\n*   All values in the input are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\dots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc148_a","tags":[],"sample_group":[["3\n1 4 8","2\n\nIf you choose $M = 3$, you will have $A = (1 \\bmod 3, 4 \\bmod 3, 8 \\bmod 3) = (1, 1, 2)$, where $A$ contains two different elements.  \nThe number of different elements in $A$ cannot become $1$, so the answer is $2$."],["4\n5 10 15 20","1\n\nIf you choose $M = 5$, you will have $A = (0, 0, 0, 0)$, which is optimal."],["10\n3785 5176 10740 7744 3999 3143 9028 2822 4748 6888","1"]],"created_at":"2026-03-03 11:01:14"}}