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.*;
import java.util.*;

public class test3 {
	static class point{
		int i;int j;
		point(int i,int  j){
			this.i = i;
			this.j = j;
		}
	}
	
static long mod = (int)10e9 +7;
	public static void main(String[] args) throws  IOException {
		FastReader f = new FastReader();
//	   int t = f.nextInt();
//	   while(t-->0) {
		  int n =f.nextInt();
		  int arr[] = new int[n];
		  for(int i = 0;i<n;i++)arr[i] = f.nextInt();
		  int sum = Integer.MAX_VALUE;
		  int curr = 0;
		  for(int i = 0;i<n;i++) {
			  if(arr[i]==1) {
			  int l = 6000,r = 6000;
			  for(int j =i-1;j>=0;j--) {
				  if(arr[j]==0) {
					  l = j;break;
				  }
			  }
			  for(int j = i+1;j<n;j++) {
				  if(arr[j]==0) {
					  r = j;break;
				  }
			  }
			  arr[Math.min(l, r)] = 2;
			  curr+=(Math.abs(i-Math.min(l, r)));
			  }
		  }
		  sum = curr;curr = 0;
		  for(int i = n-1;i>=0;i--) {
			  if(arr[i]==1) {
			  int l = 6000,r = 6000;
			  for(int j =i-1;j>=0;j--) {
				  if(arr[j]==0||arr[j]==2) {
					  l = j;break;
				  }
			  }
			  for(int j = i+1;j<n;j++) {
				  if(arr[j]==0||arr[j]==2) {
					  r = j;break;
				  }
			  }
			  arr[Math.min(l, r)] = 3;
			  curr+=(Math.abs(i-Math.min(l, r)));
			  }
		  }
		  sum = Math.min(sum, curr);
		  System.out.println(sum);
	   //}
    }
	static int GCD(int a,int b) {
		  if(a%b==0)return b;
		  else return GCD(b,a%b);
	  }
	static boolean isPrime(int n)
    {
 
        // Check if number is less than
        // equal to 1
        if (n <= 1)
            return false;
 
        // Check if number is 2
        else if (n == 2)
            return true;
 
        // Check if n is a multiple of 2
        else if (n % 2 == 0)
            return false;
 
        // If not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2)
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }
	
	static void print(int x,int y,int d,int n) {
		int i = 0;
		System.out.print(x+" "+y+" ");
			for(int j = x+d;j<y;j+=d) {
				System.out.print(j+" ");
				i++;
			}
			for(int j = x-d;j>0;j-=d) {
				if(i==n)return;
				System.out.print(j+" ");
				i++;
			}
			for(int j = y+d;j<1000000000;j+=d) {
				if(i==n)return;
				System.out.print(j+" ");
				i++;
			}
	}

	static int prime(int n){
	    int ret = 0;
	    while(n%2==0){
	        ret++;
	        n/=2;
	    }
	    for(int i=3;i<=Math.sqrt(n);i+=2){
	        while(n%i==0){
	            ret++;
	            n/=i;
	        }
	    }
	    if(n>2)ret++;
	    return ret;
	}
	static long nCr(int n, int r) 
	{ if(n<r) {
		return 0;
	} 
	    long[] C=new long[r+1]; 
	    C[0] = 1; 
	    for (int i = 1; i <= n; i++) 
	    {  
	        for (int j = Math.min(i, r); j > 0; j--) 
	            C[j] = (C[j] + C[j-1]); 
	    } 
	    return C[r]; 
	}
	static int power(int a,int n, int p)
    {
        int res = 1;
        a = a % p; 
        while (n > 0)
        {
            if ((n & 1) == 1)
                res = (res * a) % p;
            n = n >> 1; 
            a = (a * a) % p;
        }
        return res;
    }
    static boolean isPrime(int n, int k)
    {
    if (n <= 1 || n == 4) return false;
    if (n <= 3) return true;
    while (k > 0)
    {
        int a = 2 + (int)(Math.random() % (n - 4)); 
        if (power(a, n - 1, n) != 1)
            return false;
     
        k--;
        }
     
        return true;
    }
	  static long GCD(long a,long b) {
		  if(a%b==0)return b;
		  else return GCD(b,a%b);
	  }
		static ArrayList<Integer> readArray(FastReader f,int size){
			ArrayList<Integer> ret = new ArrayList<Integer>();
			for(int i=0;i<size;i++) {
				ret.add(f.nextInt());
			}return ret;
		}
	 static class FastReader 
	    { 
	        BufferedReader br; 
	        StringTokenizer st; 
	        public FastReader() 
	        { 
	            br = new BufferedReader(new
	                     InputStreamReader(System.in)); 
	        } 
	        String next() 
	        { 
	            while (st == null || !st.hasMoreElements()) 
	            { 
	                try
	                { 
	                    st = new StringTokenizer(br.readLine()); 
	                } 
	                catch (IOException  e) 
	                { 
	                    e.printStackTrace(); 
	                } 
	            } 
	            return st.nextToken(); 
	        } 
	        int nextInt() 
	        { 
	            return Integer.parseInt(next()); 
	        } 	  
	        long nextLong() 
	        { 
	            return Long.parseLong(next()); 
	        } 
	        double nextDouble() 
	        { 
	            return Double.parseDouble(next()); 
	        } 
	        String nextLine() 
	        { 
	            String str = ""; 
	            try
	            { 
	                str = br.readLine(); 
	            } 
	            catch (IOException e) 
	            { 
	                e.printStackTrace(); 
	            } 
	            return str; 
	        } 
	    }
	 

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