{"problem":{"name":"Zero or One","description":{"content":"Given an integer $N$ not less than $2$, find the number of integers $b$ not less than $2$ such that: *   when $N$ is written in base $b$, every digit is $0$ or $1$. Find the answer for $T$ independe","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc293_f"},"statements":[{"statement_type":"Markdown","content":"Given an integer $N$ not less than $2$, find the number of integers $b$ not less than $2$ such that:\n\n*   when $N$ is written in base $b$, every digit is $0$ or $1$.\n\nFind the answer for $T$ independent test cases.\nIt can be proved that there is a finite number of desired integers $b$ not less than $2$ under the constraints of this problem.\n\n## Constraints\n\n*   $1 \\leq T \\leq 1000$\n*   $2 \\leq N \\leq 10^{18}$\n*   All values in the input are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format, where $\\mathrm{test}_i$ denotes the $i$\\-th test case:\n\n$T$\n$\\mathrm{test}_1$\n$\\mathrm{test}_2$\n$\\vdots$\n$\\mathrm{test}_T$\n\nEach test case is given in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc293_f","tags":[],"sample_group":[["3\n12\n2\n36","4\n1\n5\n\nFor the first test case, four $b$'s satisfy the condition in the problem statement: $b = 2, 3, 11, 12$. Indeed, when $N=12$ is written in base $2, 3, 11$, and $12$, it becomes $1100, 110, 11$ and $10$, respectively."]],"created_at":"2026-03-03 11:01:14"}}