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.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.HashSet;
import java.util.Random;
import java.util.Set;
import java.util.StringTokenizer;

public class TaskC {
	static long mod = (long) (1000000000+7);
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader sc = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		
		int test = 1;
		while(test-->0) {
			int n = sc.nextInt();
			int[] a = new int[n];
			for(int i = 0;i<n;i++) {
				a[i] = 1-sc.nextInt();
			}
			SegTree st = new SegTree();
			st.build(a);
			
			long answer = 0;
			int[] suff = new int[n+1];
			suff[n] = 0;
			for(int i = n-1;i>=0;i--) {
				suff[i] = suff[i+1] + a[i];
			}
			Deque<Integer> deq = new ArrayDeque<>();
			for(int i = 0;i<n;i++) {
				if(a[i]==0) {
					int dist = 0;
					for(int j = i;j<n;j++) {
						if(a[j]==1) {
							break;
						}
						dist++;
					}
					int dist2 = 0;
					for(int j = i;j>=0;j--) {
						if(a[j]==1) {
							break;
						}
						dist2++;
					}
					if(dist2==0 || dist2==i+1) {
						dist2 = 100000000;
					}
					if(dist==0 || dist==n-i) {
						dist = 100000000;
					}
					int itDist = Math.min(dist, dist2);
					if(dist>=dist2) {
						a[i-itDist] = 2;
					} else {
						a[i+itDist] = 2;
					}
					answer = answer + (Math.abs(itDist));
				} else if(a[i]==1) {
					deq.add(i);
				}
			}
			out.println(answer);
		}
		
		out.close();
	}
	static class SegTree {
		
		int[] tree;
		int size;
		
		void build(int[] a) {
			init(a.length);
			build(a, 0, 0, size);
		}
		
		void build(int[] a, int x, int lx, int rx) {
			if(rx-lx==1) {
				if(lx<a.length)
					tree[x] = a[lx];
			} else {
				int m = (lx+rx)/2;
				build(a, 2*x+1, lx, m);
				build(a, 2*x+2, m, rx);
				tree[x] = tree[2*x+1] + tree[2*x+2];
			}
		}
		void init(int n) {
			size = 1;
			while(size<n) {
				size*=2;
			}
			tree = new int[2*size-1];
			for(int i = 0;i<tree.length;i++){
				tree[i] = 0;
			}
		}
		long find(int k) {
			return find(k, 0, 0, size);
		}
		long find(int k, int x, int lx, int rx) {
			if(rx==lx+1) {
				return lx;
			}
			if(tree[2*x+1]>k) {
				return find(k, 2*x+1, lx, (rx+lx)/2);
			} else {
				return find(k-tree[2*x+1], 2*x+2, (rx+lx)/2, rx);
			}
		}
		private void set(int i, int v, int x, int lx, int rx) {
			 if(rx-lx==1){
				 tree[x] = v;
				 return;
			 }
			 int m = (lx+rx)/2;
			 if(i<m) {
				 set(i, v, 2*x+1, lx, m);
			 } else {
				 set(i, v, 2*x+2, m, rx);
			 }
			 tree[x] = tree[2*x+1] + tree[2*x+2];
		}
		
		void set(int i, int v) {
			set(i, v, 0, 0, size);
		}
		
		long calc(int l, int r, int x, int lx, int rx) {
			if(l>=rx || lx>=r) {
				return 0;
			}
			
			if(lx>=l && rx<=r) {
				return tree[x];
			}
			
			int m = (lx+rx)/2;
			long s1 = calc(l, r, 2*x+1, lx, m);
			long s2 = calc(l, r, 2*x+2, m, rx);
			
			return s1+s2;
		}
		
		long calc(int l, int r) {			
			return calc(l, r, 0, 0, size);
		}
 
	}
	public static HashSet<String> getIntersection(Set<String> set1, Set<String> set2) {
	    boolean set1IsLarger = set1.size() > set2.size();
	    HashSet<String> cloneSet = new HashSet<String>(set1IsLarger ? set2 : set1);
	    cloneSet.retainAll(set1IsLarger ? set1 : set2);
	    return cloneSet;
	}
	static void shuffleArray(long[] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            long tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }   
	}
	static class FastReader {
		
		StringTokenizer st;
		BufferedReader br;
		
		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 s = "";
			while(st==null || st.hasMoreElements()) {
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return s;
		}
	}
}
