AT_abc393_d [ABC393D] Swap to Gather

You are given a string $ S $ of length $ N $ consisting of `0` and `1`. It is guaranteed that $ S $ contains at least one `1`. You may perform the following operation any number of times (possibly zero): - Choose an integer $ i $ ( $ 1 \leq i \leq N-1 $ ) and swap the $ i $ -th and $ (i+1) $ -th characters of $ S $ . Find the minimum number of operations needed so that all `1`s are contiguous. Here, all `1`s are said to be contiguous if and only if there exist integers $ l $ and $ r $ ( $ 1 \leq l \leq r \leq N $ ) such that the $ i $ -th character of $ S $ is `1` if and only if $ l \leq i \leq r $ , and `0` otherwise.

The input is given from Standard Input in the following format: > $ N $ $ S $

Print the answer.

### Sample Explanation 1 For example, the following three operations make all `1`s contiguous: - Choose $ i=2 $ and swap the 2nd and 3rd characters. Then, $ S= $ `0011001`. - Choose $ i=6 $ and swap the 6th and 7th characters. Then, $ S= $ `0011010`. - Choose $ i=5 $ and swap the 5th and 6th characters. Then, $ S= $ `0011100`. It is impossible to do this in two or fewer swaps, so the answer is $ 3 $ . ### Sample Explanation 2 All `1`s are already contiguous, so no swaps are needed. ### Constraints - $ 2 \leq N \leq 5 \times 10^5 $ - $ N $ is an integer. - $ S $ is a length $ N $ string of `0` and `1`. - $ S $ contains at least one `1`.