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.
// Created by ash_98
 
#include<bits/stdc++.h>
using namespace std;
 
#define mx 5005
#define ll long long
#define mod 1000000007
 
int ar[mx];
char ch[mx];
int n,m,ii,k;
int dp[mx][mx];
int vis[mx][mx];
vector<int>v;

int func(int i,int prv)
{
	if(i==k)return 0;
	if(prv>n)return mx*mx;
	if(vis[i][prv]==ii)return dp[i][prv];
	vis[i][prv]=ii;
	int re=func(i,prv+1);
	if(!ar[prv])re=min(re,func(i+1,prv+1)+abs(prv-v[i]));
	return dp[i][prv]=re;
}
 
void solve()
{
	scanf("%d",&n);
	v.clear();
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&ar[i]);
		if(ar[i])v.push_back(i);
	}
	ii++;
	k=v.size();
	printf("%d\n",func(0,1));


}
 
int main()
{
	int t=1;
	//scanf("%d",&t);
	while(t--)solve();
	return 0;
}