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.util.*;
import java.lang.*;
import java.io.*;

public class D {

//		            ***                          ++                      
//	             +=-==+                      +++=-                     
//	            +-:---==+                   *+=----=                   
//	           +-:------==+               ++=------==                  
//	           =-----------=++=========================                
//	          +--:::::---:-----============-=======+++====             
//	          +---:..:----::-===============-======+++++++++           
//	          =---:...---:-===================---===++++++++++         
//	          +----:...:-=======================--==+++++++++++        
//	          +-:------====================++===---==++++===+++++      
//	         +=-----======================+++++==---==+==-::=++**+     
//	        +=-----================---=======++=========::.:-+*****    
//	       +==::-====================--:  --:-====++=+===:..-=+*****   
//	       +=---=====================-...  :=..:-=+++++++++===++*****  
//	       +=---=====+=++++++++++++++++=-:::::-====+++++++++++++*****+ 
//	      +=======++++++++++++=+++++++============++++++=======+****** 
//	      +=====+++++++++++++++++++++++++==++++==++++++=:...  . .+**** 
//	     ++====++++++++++++++++++++++++++++++++++++++++-.     ..-+**** 
//	     +======++++++++++++++++++++++++++++++++===+====:.    ..:=++++ 
//	     +===--=====+++++++++++++++++++++++++++=========-::....::-=++* 
//	     ====--==========+++++++==+++===++++===========--:::....:=++*  
//	     ====---===++++=====++++++==+++=======-::--===-:.  ....:-+++   
//	     ==--=--====++++++++==+++++++++++======--::::...::::::-=+++    
//	     ===----===++++++++++++++++++++============--=-==----==+++     
//	     =--------====++++++++++++++++=====================+++++++     
//	     =---------=======++++++++====+++=================++++++++     
//	     -----------========+++++++++++++++=================+++++++    
//	     =----------==========++++++++++=====================++++++++  
//	     =====------==============+++++++===================+++==+++++ 
//	     =======------==========================================++++++

	// created by : Nitesh Gupta

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringBuilder sb = new StringBuilder();
		String[] scn = (br.readLine()).trim().split(" ");
		int n = Integer.parseInt(scn[0]);
		long[] arr = new long[n];
		boolean[] vis = new boolean[n];
		scn = (br.readLine()).trim().split(" ");
		zeros = new ArrayList<>();
		ones = new ArrayList<>();

		long[][] dp = new long[n + 2][n + 2];

		for (int i = 0; i < n; i++) {
			arr[i] = Long.parseLong(scn[i]);
			if (arr[i] == 1) {
				vis[i] = true;
				ones.add(i);
			} else {
				zeros.add(i);
			}
		}
		int x = ones.size();
		int y = zeros.size();

// source: https://math.stackexchange.com/questions/414182/finding-minimum-sum-of-absolute-differences-betweens-values-of-two-sets/536050

		for (int i = 1; i <= x; i++) {
			dp[i][y + 1] = (long) (1e15);
		}

		for (int i = x + 1; i <= n; i++) {
			for (int j = 1; j <= n + 1; j++) {
				dp[i][j] = 0;
			}
		}
		dp[x + 1][y + 1] = 0;

//		Base cases:
//
//			dp[length of arr1][length of arr2] = 0
//			dp[A][length of arr2] = infinity (it's impossible to pair the remaining elements of arr1).
//			
		for (int i = x; i > 0; i--) {

			for (int j = y; j > 0; j--) {

				dp[i][j] = dp[i][j + 1];

				if (i <= x && j <= y) {
					long curr = Math.abs(ones.get(i - 1) - zeros.get(j - 1));
					dp[i][j] = Math.min(curr + dp[i + 1][j + 1], dp[i][j]);
				}
			}
		}
		sb.append(dp[1][1]);

		sb.append("\n");
		System.out.println(sb);
		return;

	}

	static ArrayList<Integer> zeros;
	static ArrayList<Integer> ones;
	static long res;

	public static void rec(int i, int n, int m, boolean[] vis, long[][] dp) {

	}

	public static void sort(long[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			long temp = arr[i];
			arr[i] = arr[idx];
			arr[idx] = temp;
		}
		Arrays.sort(arr);
	}

	public static void sort(int[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			int temp = arr[i];
			arr[i] = arr[idx];
			arr[idx] = temp;
		}
		Arrays.sort(arr);
	}

	public static void print(long[][] dp) {
		for (long[] a : dp) {
			for (long ele : a) {
				System.out.print(ele + " ");
			}
			System.out.println();
		}
	}

	public static void print(int[][] dp) {
		for (int[] a : dp) {
			for (int ele : a) {
				System.out.print(ele + " ");
			}
			System.out.println();
		}
	}

	public static void print(boolean[] dp) {
		for (boolean ele : dp) {
			System.out.print(ele + " ");
		}
		System.out.println();
	}

	public static void print(long[] dp) {
		for (long ele : dp) {
			System.out.print(ele + " ");
		}
		System.out.println();
	}

}
