{"problem":{"name":"Sum equals LCM","description":{"content":"You are given a positive integer $N$. Determine if there are two or more (not necessarily distinct) positive integers $A_1,A_2,\\dots,A_n\\ (2 \\leq n)$ that satisfy all of the following conditions: *  ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc165_a"},"statements":[{"statement_type":"Markdown","content":"You are given a positive integer $N$.\nDetermine if there are two or more (not necessarily distinct) positive integers $A_1,A_2,\\dots,A_n\\ (2 \\leq n)$ that satisfy all of the following conditions:\n\n*   $A_1+A_2+\\dots+A_n=N$.\n*   The least common multiple of $A_1,A_2,\\dots,A_n$ is $N$.\n\nYou have $T$ test cases to solve.\n\n## Constraints\n\n*   $1 \\leq T \\leq 100$\n*   $2 \\leq N \\leq 10^{9}$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$T$\n$\\mathrm{case}_1$\n$\\vdots$\n$\\mathrm{case}_T$\n\nEach case is given in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc165_a","tags":[],"sample_group":[["4\n6\n4\n998244353\n367291763","Yes\nNo\nNo\nYes\n\nFor the first test case, three positive integers $(A_1,A_2,A_3)=(1,2,3)$, for example, have $A_1+A_2+A_3=1+2+3=6$, and the least common multiple of $A_1,A_2,A_3$ is $6$, satisfying the conditions.\nFor the second test case, no two or more positive integers satisfy the conditions."]],"created_at":"2026-03-03 11:01:13"}}