{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $2 \\leq N \\leq 10^5$\n*   $1 \\leq A_i \\leq 10^9$"},{"iden":"output","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $...$ $A_N$"},{"iden":"output","content":"Print the maximum possible greatest common divisor of the $N$ integers on the blackboard after your move."},{"iden":"sample input 1","content":"3\n7 6 8"},{"iden":"sample output 1","content":"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."},{"iden":"sample input 2","content":"3\n12 15 18"},{"iden":"sample output 2","content":"6"},{"iden":"sample input 3","content":"2\n1000000000 1000000000"},{"iden":"sample output 3","content":"1000000000\n\nWe can replace an integer with itself."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}