{"problem":{"name":"Binary Programming","description":{"content":"Takahashi has an empty string $S$ and a variable $x$ whose initial value is $0$. Also, we have a string $T$ consisting of `0` and `1`. Now, Takahashi will do the operation with the following two steps","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"nomura2020_e"},"statements":[{"statement_type":"Markdown","content":"Takahashi has an empty string $S$ and a variable $x$ whose initial value is $0$.\nAlso, we have a string $T$ consisting of `0` and `1`.\nNow, Takahashi will do the operation with the following two steps $|T|$ times.\n\n*   Insert a `0` or a `1` at any position of $S$ of his choice.\n*   Then, increment $x$ by the sum of the digits in the odd positions (first, third, fifth, ...) of $S$. For example, if $S$ is `01101`, the digits in the odd positions are `0`, `1`, `1` from left to right, so $x$ is incremented by $2$.\n\nPrint the maximum possible final value of $x$ in a sequence of operations such that $S$ equals $T$ in the end.\n\n## Constraints\n\n*   $1 \\leq |T| \\leq 2 \\times 10^5$\n*   $T$ consists of `0` and `1`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$T$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"nomura2020_e","tags":[],"sample_group":[["1101","5\n\nBelow is one sequence of operations that maximizes the final value of $x$ to $5$.\n\n*   Insert a `1` at the beginning of $S$. $S$ becomes `1`, and $x$ is incremented by $1$.\n*   Insert a `0` to the immediate right of the first character of $S$. $S$ becomes `10`, and $x$ is incremented by $1$.\n*   Insert a `1` to the immediate right of the second character of $S$. $S$ becomes `101`, and $x$ is incremented by $2$.\n*   Insert a `1` at the beginning of $S$. $S$ becomes `1101`, and $x$ is incremented by $1$."],["0111101101","26"]],"created_at":"2026-03-03 11:01:14"}}