{"problem":{"name":"GCD on Blackboard","description":{"content":"There are $N$ integers, $A_1, A_2, ..., A_N$, written on the blackboard. You will choose one of them and replace it with an integer of your choice between $1$ and $10^9$ (inclusive), possibly the same","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc125_c"},"statements":[{"statement_type":"Markdown","content":"There are $N$ integers, $A_1, A_2, ..., A_N$, written on the blackboard.\nYou will choose one of them and replace it with an integer of your choice between $1$ and $10^9$ (inclusive), possibly the same as the integer originally written.\nFind the maximum possible greatest common divisor of the $N$ integers on the blackboard after your move.\n\n## Constraints\n\n*   All values in input are integers.\n*   $2 \\leq N \\leq 10^5$\n*   $1 \\leq A_i \\leq 10^9$\n\n## Output\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $...$ $A_N$\n\n[samples]\n\n## Output\n\nPrint the maximum possible greatest common divisor of the $N$ integers on the blackboard after your move.","is_translate":false,"language":"English"}],"meta":{"iden":"abc125_c","tags":[],"sample_group":[["3\n7 6 8","2\n\nIf we replace $7$ with $4$, the greatest common divisor of the three integers on the blackboard will be $2$, which is the maximum possible value."],["3\n12 15 18","6"],["2\n1000000000 1000000000","1000000000\n\nWe can replace an integer with itself."]],"created_at":"2026-03-03 11:01:14"}}