Balanced String

给你一个长为 $n$ 的 $01$ 字符串，每次操作交换两个元素，求最少几次操作能使字符串的顺序对个数与逆序对个数相等。

You are given a binary string $ s $ (a binary string is a string consisting of characters 0 and/or 1). Let's call a binary string balanced if the number of subsequences 01 (the number of indices $ i $ and $ j $ such that $ 1 \le i < j \le n $ , $ s_i=0 $ and $ s_j=1 $ ) equals to the number of subsequences 10 (the number of indices $ k $ and $ l $ such that $ 1 \le k < l \le n $ , $ s_k=1 $ and $ s_l=0 $ ) in it. For example, the string 1000110 is balanced, because both the number of subsequences 01 and the number of subsequences 10 are equal to $ 6 $ . On the other hand, 11010 is not balanced, because the number of subsequences 01 is $ 1 $ , but the number of subsequences 10 is $ 5 $ . You can perform the following operation any number of times: choose two characters in $ s $ and swap them. Your task is to calculate the minimum number of operations to make the string $ s $ balanced.

The only line contains the string $ s $ ( $ 3 \le |s| \le 100 $ ) consisting of characters 0 and/or 1. Additional constraint on the input: the string $ s $ can be made balanced.

Print a single integer — the minimum number of swap operations to make the string $ s $ balanced.

101

0

1000110

0

11010

1

11001100

2

In the first example, the string is already balanced, the number of both 01 and 10 is equal to $ 1 $ . In the second example, the string is already balanced, the number of both 01 and 10 is equal to $ 6 $ . In the third example, one of the possible answers is the following one: 11010 $ \rightarrow $ 01110. After that, the number of both 01 and 10 is equal to $ 3 $ . In the fourth example, one of the possible answers is the following one: 11001100 $ \rightarrow $ 11001010 $ \rightarrow $ 11000011. After that, the number of both 01 and 10 is equal to $ 8 $ .