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.
#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
using namespace std;
int dp[5010][5010];
int a[5010];
int b[5010];
int c[5010];
signed main() {
	ios::sync_with_stdio(0);
	int n;
	cin >> n;
	for (int i = 1; i <= n; i++)cin >> a[i];
	int tot = 0;
	int cnt = 0;
	for (int i = 1; i <= n; i++) {
		if (a[i])b[++tot] = i;
		else c[++cnt] = i;
	}
	for (int i = 1; i <= tot; i++)dp[i][i] = dp[i - 1][i - 1] + abs(b[i] - c[i]);
	for (int i = 1; i <= tot; i++) {
		for (int j = i + 1; j <= cnt; j++) {
			dp[i][j] = min(dp[i][j - 1], dp[i - 1][j - 1] + abs(b[i] - c[j]));
		}
	}
	cout << dp[tot][cnt] << endl;
	return 0;
}