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.
// package codeforces;

import java.util.*;

public class ArmChairs {
	static int[]arr;
	static ArrayList<Integer>a;
	static ArrayList<Integer>b;
	static int dp[][];
	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		arr=new int[n];
		for(int i=0;i<n;i++) {
			arr[i]=scn.nextInt();
		}
		dp=new int[n+1][n+1];
		a =new ArrayList<>();
		b =new ArrayList<>();
		for(int i=0;i<n;i++) {
			if(arr[i]==0) {
				a.add(i);
			}else{
				b.add(i);
			}
		}
		System.out.println(solve(0,0));	
	}
	
	public static int solve(int i,int j) {
		if(i==b.size()) {
			return 0;
		}
		if(j==a.size()) {
			return 100000000;
		}

		if(dp[i][j]!=0) {
			return dp[i][j];
		}
		int x=Math.abs(a.get(j)-b.get(i))+solve(i+1,j+1);
		int y=solve(i,j+1);
		return dp[i][j]=Math.min(x, y);
	}
	

}
