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 n,a[5001],t[5001],num,f[5001][5001];
int read(){
	int w=0,f=1;
	char c=getchar();
	while (c>'9'||c<'0'){
		if (c=='-') f=-1;
		c=getchar();
	}
	while (c>='0'&&c<='9'){
		w=(w<<1)+(w<<3)+(c^48);
		c=getchar();
	}
	return w*f;
}
int main(){
	memset(f,0x3f,sizeof(f));
	n=read();
	f[0][0]=0;
	for (int i=1;i<=n;i++){
		a[i]=read();
		f[0][i]=0;
	}
	for (int i=1;i<=n;i++) if(a[i]) t[++num]=i;
    for (int i=1;i<=num;i++){
    	for (int j=1;j<=n;j++){
        	f[i][j]=f[i][j-1];
			if(!a[j])
				f[i][j]=min(f[i][j],f[i-1][j-1]+abs(t[i]-j));
    	}
	}
	printf("%d\n",f[num][n]);
	return 0;
}