{"raw_statement":[{"iden":"problem statement","content":"$N$ cells are arranged in a row. Some of them may contain tokens. You are given a string $s$ that consists of `0`s and `1`s. If the $i$\\-th character of $s$ is `1`, the $i$\\-th cell (from left) contains a token. Otherwise, it doesn't contain a token.\nSnuke wants to perform the following operation as many times as possible. In each operation, he chooses three consecutive cells. Let's call the cells $X, Y, Z$ from left to right. In order for the operation to be valid, both $X$ and $Z$ must contain tokens and $Y$ must not contain a token. Then, he removes these two tokens and puts a new token on $Y$.\nHow many operations can he perform if he performs operations in the optimal way?"},{"iden":"constraints","content":"*   $1 \\leq N \\leq 500,000$\n*   $|s| = N$\n*   Each character in $s$ is either `0` or `1`."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$s$"},{"iden":"sample input 1","content":"7\n1010101"},{"iden":"sample output 1","content":"2\n\nFor example, he can perform two operations in the following way:\n\n*   Perform an operation on the last three cells. Now the string that represents tokens becomes `1010010`.\n*   Perform an operation on the first three cells. Now the string that represents tokens becomes `0100010`.\n\nNote that the choice of operations matters. For example, if he chooses three cells in the middle first, he can perform no more operations."},{"iden":"sample input 2","content":"50\n10101000010011011110001001111110000101010111100110"},{"iden":"sample output 2","content":"10"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}