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 com.wissamfawaz;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
 
public class D {
    static final long MOD = 1000000007L;
    //static final long MOD2 = 1000000009L;
    //static final long MOD = 998244353L;
    //static final long INF = 500000000000L;
    static final int INF = 10000000;
    static final int NINF = -100000;
    static FastScanner sc;
    static PrintWriter pw;
 
    public static void main2(String[] args) {
        sc = new FastScanner();
        pw = new PrintWriter(System.out);
        
        //int Q = sc.ni();
        //for (int q = 0; q < Q; q++) {
        
        int l = 1, r = 1_000_000;
        while(l != r) {
        	int mid = (l + r + 1)/2;
        	pw.println(mid);
        	pw.flush();
        	
        	String response = sc.nextLine();
        	if(response.equals("<")) {
        		r = mid-1;
        	} else {
        		l = mid;
        	}
        }
        
        pw.println("! " + l);
        pw.flush();
        //}
        //pw.close();
    }
    
    public static void main(String[] args) {
        sc = new FastScanner();
        pw = new PrintWriter(System.out);
        
        //int Q = sc.ni();
        //for (int q = 0; q < Q; q++) {
        int n = sc.ni();
        int[] arr = sc.intArray(n);
        
        int nbZeros = 0;
        int nbOnes = 0;
        for(int i=0; i<n; i++) {
        	if(arr[i] == 0) {
        		nbZeros++;
        	} else {
        		nbOnes++;
        	}
        }
        
        if(nbZeros == n) {
        	pw.println(0);
        } else {
        	int[] ones = new int[nbOnes];
        	int[] zeros = new int[nbZeros];
        	int idxZeros = 0;
        	int idxOnes = 0;
        	for(int i=0; i<n; i++) {
        		if(arr[i] == 0) {
        			zeros[idxZeros++] = i;
        		} else {
        			ones[idxOnes++] = i;
        		}
        	}
        	
        	int[][] dp = new int[ones.length+1][zeros.length+1];
        	
        	
        	for(int i=0; i<dp.length; i++) {
        		dp[i][zeros.length] = 250_000_000;
        	}
        	
        	for(int j=0; j<dp[0].length; j++) {
        		dp[ones.length][j] = 250_000_000;
        	}
        	
        	dp[ones.length][zeros.length] = 0;
        	for(int i=dp.length-2; i>=0; i--) {
        		for(int j=dp[0].length-2; j>=0; j--) {
        			dp[i][j] = Math.min(Math.abs(ones[i]-zeros[j])+dp[i+1][j+1], dp[i][j+1]);
        		}
        	}
        	
        	pw.println(dp[0][0]);
        }
        
        
        //}
        pw.close();
    }
 
    
    
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in), 32768);
            st = null;
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int ni() {
            return Integer.parseInt(next());
        }
 
        int[] intArray(int N) {
            int[] ret = new int[N];
            for (int i = 0; i < N; i++)
                ret[i] = ni();
            return ret;
        }
 
        long nl() {
            return Long.parseLong(next());
        }
 
        long[] longArray(int N) {
            long[] ret = new long[N];
            for (int i = 0; i < N; i++)
                ret[i] = nl();
            return ret;
        }
 
        double nd() {
            return Double.parseDouble(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
	