Balanced Substring

You are given a string s consisting only of characters 0 and 1. A substring [l, r] of s is a string s_ls_l + 1s_l + 2... s_r, and its length equals to r - l + 1. A substring is called balanced if the number of zeroes (0) equals to the number of ones in this substring.

You have to determine the length of the longest balanced substring of s.

Input

The first line contains n (1 ≤ n ≤ 100000) — the number of characters in s.

The second line contains a string s consisting of exactly n characters. Only characters 0 and 1 can appear in s.

Output

If there is no non-empty balanced substring in s, print 0. Otherwise, print the length of the longest balanced substring.

Example

Input

8
11010111

Output

4

Input

3
111

Output

0

Note

In the first example you can choose the substring [3, 6]. It is balanced, and its length is 4. Choosing the substring [2, 5] is also possible.

In the second example it's impossible to find a non-empty balanced substring.

求前缀和，然后map一下，前缀和相同的表示两位置之间的字符串达到了平衡。

代码：

#include <iostream>
#include <string>
#include <map>
using namespace std;
int s[100001];
int main()
{
    int n;
    string a;
    cin>>n;
    cin>>a;
    map<int,int>q;
    int sum = 0,maxi = 0;
    for(int i = 0;i < n;i ++)
    {
        if(a[i] == '0')sum += -1;
        else sum += 1;
        if(!q[sum]&&sum)q[sum] = i + 1;//如果sum为0表示本来就平衡不需要标记了
        else
        {
            maxi = max(maxi,i - q[sum] + 1);
        }
    }
    cout<<maxi;
}