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;
using ll = long long;
using pii = pair<int,int>;
const int INF = 1e9;
const int MOD = 1e9+7;
vector<int>zero;
vector<int>one;
ll dp[5000][5000];
int solve(int i,int j,int n,int m){
	if(i>=n)
		return 0;
	int req = n-i;
	int av = m-j;
	if(req>av)
		return INF;
	if(dp[i][j]!=-1)
		return dp[i][j];
	int ans1 = solve(i,j+1,n,m);
	int ans2 = abs(one[i]-zero[j])+solve(i+1,j+1,n,m);
	return dp[i][j] = min(ans1,ans2);
}
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int n;
	cin>>n;
	for(int i = 0;i<n;i++){
		int a;
		cin>>a;
		if(a==1)
			one.push_back(i);
		else
			zero.push_back(i);
	}
	memset(dp,-1,sizeof dp);
	int n1 = one.size();
	int m = zero.size();
	cout<<solve(0,0,n1,m);
}