There are n armchairs, numbered from 1 to n from left to right. Some armchairs are occupied by people (at most one person per armchair), others are not. The number of occupied armchairs is not greater than n/2.

For some reason, you would like to tell people to move from their armchairs to some other ones. If the i-th armchair is occupied by someone and the j-th armchair is not, you can tell the person sitting in the i-th armchair to move to the j-th armchair. The time it takes a person to move from the i-th armchair to the j-th one is |i - j| minutes. You may perform this operation any number of times, but these operations must be done sequentially, i. e. you cannot tell a person to move until the person you asked to move in the last operation has finished moving to their destination armchair.

You want to achieve the following situation: every seat that was initially occupied must be free. What is the minimum time you need to do it?

Input

The first line contains one integer n (2 ≤ n ≤ 5000) — the number of armchairs.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 1). a_i = 1 means that the i-th armchair is initially occupied, a_i = 0 means that it is initially free. The number of occupied armchairs is at most n/2.

Output

Print one integer — the minimum number of minutes you have to spend to achieve the following situation: every seat that was initially occupied must be free.

Examples

Input


7
1 0 0 1 0 0 1


Output


3


Input


6
1 1 1 0 0 0


Output


9


Input


5
0 0 0 0 0


Output


0

Note

In the first test, you can perform the following sequence:

  1. ask a person to move from armchair 1 to armchair 2, it takes 1 minute; 
  2. ask a person to move from armchair 7 to armchair 6, it takes 1 minute; 
  3. ask a person to move from armchair 4 to armchair 5, it takes 1 minute. 



In the second test, you can perform the following sequence:

  1. ask a person to move from armchair 1 to armchair 4, it takes 3 minutes; 
  2. ask a person to move from armchair 2 to armchair 6, it takes 4 minutes; 
  3. ask a person to move from armchair 4 to armchair 5, it takes 1 minute; 
  4. ask a person to move from armchair 3 to armchair 4, it takes 1 minute. 



In the third test, no seat is occupied so your goal is achieved instantly.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int x;
  cin >> x;
  while (x) {
    int n, i, j, t;
    cin >> n;
    long long m, a[3][n];
    cin >> m;
    memset(a, -1, sizeof a);
    for (i = 0; i < n; i++) cin >> a[0][i];
    char s[n];
    for (i = 0; i < n; i++) {
      cin >> s[i];
      if (s[i] == 'R') a[1][i] = 1;
    }
    t = 0;
    while (t <= 2 * n) {
      t++;
      for (i = 0; i < n; i++) a[0][i] += a[1][i];
      for (i = 0; i < n - 1; i++)
        for (j = i + 1; j < n; j++) {
          if (a[0][i] == a[0][j]) {
            if ((a[2][i] == -1 || a[2][i] == t) &&
                (a[2][j] == -1 || a[2][j] == t)) {
              a[2][j] = t;
              a[2][i] = t;
            }
          }
        }
      for (i = 0; i < n; i++)
        if (a[0][i] == m || a[0][i] == 0) {
          a[1][i] *= -1;
        }
    }
    for (i = 0; i < n; i++) cout << a[2][i] << " ";
    cout << '\n';
    x--;
  }
}
