{"problem":{"name":"Divide by 2 or 3","description":{"content":"You are given a sequence of positive integers: $A=(a_1,a_2,\\ldots,a_N)$.   You can choose and perform one of the following operations any number of times, possibly zero. *   Choose an integer $i$ suc","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc276_d"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence of positive integers: $A=(a_1,a_2,\\ldots,a_N)$.  \nYou can choose and perform one of the following operations any number of times, possibly zero.\n\n*   Choose an integer $i$ such that $1 \\leq i \\leq N$ and $a_i$ is a multiple of $2$, and replace $a_i$ with $\\frac{a_i}{2}$.\n*   Choose an integer $i$ such that $1 \\leq i \\leq N$ and $a_i$ is a multiple of $3$, and replace $a_i$ with $\\frac{a_i}{3}$.\n\nYour objective is to make $A$ satisfy $a_1=a_2=\\ldots=a_N$.  \nFind the minimum total number of times you need to perform an operation to achieve the objective. If there is no way to achieve the objective, print `-1` instead.\n\n## Constraints\n\n*   $2 \\leq N \\leq 1000$\n*   $1 \\leq a_i \\leq 10^9$\n*   All values in the input are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $\\ldots$ $a_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc276_d","tags":[],"sample_group":[["3\n1 4 3","3\n\nHere is a way to achieve the objective in three operations, which is the minimum needed.\n\n*   Choose an integer $i=2$ such that $a_i$ is a multiple of $2$, and replace $a_2$ with $\\frac{a_2}{2}$. $A$ becomes $(1,2,3)$.\n*   Choose an integer $i=2$ such that $a_i$ is a multiple of $2$, and replace $a_2$ with $\\frac{a_2}{2}$. $A$ becomes $(1,1,3)$.\n*   Choose an integer $i=3$ such that $a_i$ is a multiple of $3$, and replace $a_3$ with $\\frac{a_3}{3}$. $A$ becomes $(1,1,1)$."],["3\n2 7 6","\\-1\n\nThere is no way to achieve the objective."],["6\n1 1 1 1 1 1","0"]],"created_at":"2026-03-03 11:01:13"}}