{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $0 \\leq A_i \\leq 10^9$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\dots$ $A_N$"},{"iden":"sample input 1","content":"3\n1 4 8"},{"iden":"sample output 1","content":"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 $2$."},{"iden":"sample input 2","content":"4\n5 10 15 20"},{"iden":"sample output 2","content":"1\n\nIf you choose $M = 5$, you will have $A = (0, 0, 0, 0)$, which is optimal."},{"iden":"sample input 3","content":"10\n3785 5176 10740 7744 3999 3143 9028 2822 4748 6888"},{"iden":"sample output 3","content":"1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}