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<iostream>
#include<algorithm>
#include<cmath>
#include<cstdio>
#include<string>
#include<cstring>
#include<queue>
#include<vector>
#include<stack>
#include<map>
#define ll long long

using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 1e6+5;

int a[maxn],y[maxn],my[maxn],ycnt = 0,mycnt = 0;
int dp[5005][5005]; 
int main()
{
	int n; cin>>n;
	for(int i = 1; i <= n;i++)  {
		cin>>a[i];
		if(a[i]) y[++ycnt] = i;
		else     my[++mycnt] = i; 
	}
	dp[0][0] = 0;
	for(int i = 1; i <= ycnt; i++) {
		dp[i][i] = dp[i-1][i-1]+abs(y[i]-my[i]);
		for(int j = i+1; j <= mycnt; j++) {
			dp[i][j] = min(dp[i][j-1],dp[i-1][j-1]+abs(y[i]-my[j]));
		}
	}
	if(!ycnt) puts("0");else
	cout<<dp[ycnt][mycnt]<<"\n";
	return 0;
}

