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.

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.TreeSet;

import java.util.Iterator;

public class First {

	public static void main(String[] args) {
		FastScanner fs = new FastScanner();
		int T = 1;
		for (int tt = 0; tt < T; tt++) {

			int n=fs.nextInt();
			PriorityQueue<Integer> pq=new PriorityQueue<>();
			int[] arr=new int[n];
			int spotsDone=0;
			int ones=0;
			for(int i=0;i<n;++i)
			{
				arr[i]=fs.nextInt();
				if(arr[i]==0)
				{
					pq.add(i);

				}
				else
				{
					spotsDone++;
					ones++;
				}
			}
			//System.out.println(pq);
			int ans=0;
			
			for(int i=0;i<n;++i)
			{
				if(arr[i]==1)
				{
					ones--;
					int x=pq.poll();
					while(!pq.isEmpty() && Math.abs(i-x) > Math.abs(i-pq.peek()) && pq.size()>ones)
					{
						x=pq.poll();
					}
					ans+=(Math.abs(i-x));
				}
			}

			System.out.println(ans);
		}
	}
	static int solve()
	{
		return 0;
	}
	static int MOD=(int)(1e9+7);
    static void debug1(int[] arr)
    {
        for(int i=0;i<arr.length;++i)
            System.out.print(arr[i]+" ");
        System.out.println();
    }
    static void debug2(int[][] arr)
    {
        for(int i=0;i<arr.length;++i)
        	for(int j=0;j<arr[0].length;++j)
        		System.out.println(arr[i][j]+" ");
        System.out.println();
    }

    static int[] take1(int n, FastScanner fs)
    {
        int[] arr=new int[n];
        for(int i=0;i<n;++i)
            arr[i]=fs.nextInt();
        return arr;
    } 
    static int[][] take2(int m, int n, FastScanner fs)
    {
        int[][] arr=new int[m][n];
        for(int i=0;i<m;++i)
            for(int j=0;j<n;++j)
                arr[i][j]=fs.nextInt();
        return arr;
    } 
	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}


}