{"problem":{"name":"Base -2 Number","description":{"content":"Given an integer $N$, find the base $-2$ representation of $N$. Here, $S$ is the base $-2$ representation of $N$ when the following are all satisfied: *   $S$ is a string consisting of `0` and `1`. *","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc105_c"},"statements":[{"statement_type":"Markdown","content":"Given an integer $N$, find the base $-2$ representation of $N$.\nHere, $S$ is the base $-2$ representation of $N$ when the following are all satisfied:\n\n*   $S$ is a string consisting of `0` and `1`.\n*   Unless $S =$ `0`, the initial character of $S$ is `1`.\n*   Let $S = S_k S_{k-1} ... S_0$, then $S_0 \\times (-2)^0 + S_1 \\times (-2)^1 + ... + S_k \\times (-2)^k = N$.\n\nIt can be proved that, for any integer $M$, the base $-2$ representation of $M$ is uniquely determined.\n\n## Constraints\n\n*   Every value in input is integer.\n*   $-10^9 \\leq N \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc105_c","tags":[],"sample_group":[["\\-9","1011\n\nAs $(-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9$, `1011` is the base $-2$ representation of $-9$."],["123456789","11000101011001101110100010101"],["0","0"]],"created_at":"2026-03-03 11:01:14"}}