{"raw_statement":[{"iden":"problem statement","content":"You are given an integer $K$ greater than or equal to $2$.  \nFind the minimum positive integer $N$ such that $N!$ is a multiple of $K$.\nHere, $N!$ denotes the factorial of $N$. Under the Constraints of this problem, we can prove that such an $N$ always exists."},{"iden":"constraints","content":"*   $2\\leq K\\leq 10^{12}$\n*   $K$ is an integer."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$K$"},{"iden":"sample input 1","content":"30"},{"iden":"sample output 1","content":"5\n\n*   $1!=1$\n*   $2!=2\\times 1=2$\n*   $3!=3\\times 2\\times 1=6$\n*   $4!=4\\times 3\\times 2\\times 1=24$\n*   $5!=5\\times 4\\times 3\\times 2\\times 1=120$\n\nTherefore, $5$ is the minimum positive integer $N$ such that $N!$ is a multiple of $30$. Thus, $5$ should be printed."},{"iden":"sample input 2","content":"123456789011"},{"iden":"sample output 2","content":"123456789011"},{"iden":"sample input 3","content":"280"},{"iden":"sample output 3","content":"7"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}