{"raw_statement":[{"iden":"problem statement","content":"There are $N$ integers $A_1, A_2, A_3, \\dots, A_N$ written on a blackboard.  \nYou will do the following operation $N - 1$ times:\n\n*   Choose two numbers written on the blackboard and erase them. Let $x$ and $y$ be the erased numbers. Then, write $\\gcd(x, y)$ or $\\min(x, y)$ on the blackboard.\n\nAfter $N - 1$ operations, just one integer will remain on the blackboard. How many possible values of this number are there?"},{"iden":"constraints","content":"*   $2 \\le N \\le 2000$\n*   $1 \\le A_i \\le 10^9$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $A_3$ $\\dots$ $A_N$"},{"iden":"sample input 1","content":"3\n6 9 12"},{"iden":"sample output 1","content":"2\n\nThe possible values of the last remaining number are $3$ and $6$.  \nWe will have $3$ in the end if, for example, we do as follows:\n\n*   choose $9, 12$ and erase them from the blackboard, then write $\\gcd(9, 12) = 3$;\n*   choose $6, 3$ and erase them from the blackboard, then write $\\min(6, 3) = 3$.\n\nAlso, we will have $6$ in the end if, for example, we do as follows:\n\n*   choose $6, 12$ and erase them from the blackboard, then write $\\gcd(6, 12) = 6$;\n*   choose $6, 9$ and erase them from the blackboard, then write $\\min(6, 9) = 6$."},{"iden":"sample input 2","content":"4\n8 2 12 6"},{"iden":"sample output 2","content":"1\n\n$2$ is the only number that can remain on the blackboard."},{"iden":"sample input 3","content":"7\n30 28 33 49 27 37 48"},{"iden":"sample output 3","content":"7\n\n$1$, $2$, $3$, $4$, $6$, $7$, and $27$ can remain on the blackboard."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}