{"raw_statement":[{"iden":"problem statement","content":"Given are $N$ positive integers $A_1,...,A_N$.\nConsider positive integers $B_1, ..., B_N$ that satisfy the following condition.\nCondition: For any $i, j$ such that $1 \\leq i < j \\leq N$, $A_i B_i = A_j B_j$ holds.\nFind the minimum possible value of $B_1 + ... + B_N$ for such $B_1,...,B_N$.\nSince the answer can be enormous, print the sum modulo ($10^9 +7$)."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^4$\n*   $1 \\leq A_i \\leq 10^6$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $...$ $A_N$"},{"iden":"sample input 1","content":"3\n2 3 4"},{"iden":"sample output 1","content":"13\n\nLet $B_1=6$, $B_2=4$, and $B_3=3$, and the condition will be satisfied."},{"iden":"sample input 2","content":"5\n12 12 12 12 12"},{"iden":"sample output 2","content":"5\n\nWe can let all $B_i$ be $1$."},{"iden":"sample input 3","content":"3\n1000000 999999 999998"},{"iden":"sample output 3","content":"996989508\n\nPrint the sum modulo $(10^9+7)$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}