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.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public final class D {

    private static class SegTree {
        int leftMost, rightMost;
        SegTree left, right;
        int min;

        SegTree(int leftMost, int rightMost, int[] arr) {
            this.leftMost = leftMost;
            this.rightMost = rightMost;
            if (leftMost == rightMost) {
                min = arr[leftMost];
            } else {
                final int mid = leftMost + rightMost >>> 1;
                left = new SegTree(leftMost, mid, arr);
                right = new SegTree(mid + 1, rightMost, arr);
                recalc();
            }
        }

        private void recalc() {
            if (leftMost == rightMost) {
                return;
            }
            min = Math.min(left.min, right.min);
        }

        // rightMost index that is < r and where arr[idx] < k
        private int query1(int k, int r) {
            if (min >= k || leftMost >= r) {
                return -1;
            }
            if (leftMost == rightMost) {
                return leftMost;
            }
            final int resR = right.query1(k, r);
            return resR != -1 ? resR : left.query1(k, r);
        }

        // leftMost index that is > l and where arr[idx] < k
        private int query2(int k, int l) {
            if (min >= k || rightMost <= l) {
                return -1;
            }
            if (leftMost == rightMost) {
                return leftMost;
            }
            final int resL = left.query2(k, l);
            return resL != -1 ? resL : right.query2(k, l);
        }

        private void update(int idx, int val) {
            if (leftMost == rightMost) {
                min = val;
            } else {
                final int mid = leftMost + rightMost >>> 1;
                if (idx <= mid) {
                    left.update(idx, val);
                } else {
                    right.update(idx, val);
                }
                recalc();
            }
        }
    }

    static SegTree st;
    static int[][] dp;

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        final int n = fs.nextInt();
        final int[] arr = fs.nextIntArray(n);
        st = new SegTree(0, n - 1, arr);
        dp = new int[n + 1][n];
        for (int[] row: dp) {
            Arrays.fill(row, -1);
        }
        System.out.println(dfs(arr, -1, 0));
    }

    private static int dfs(int[] arr, int prev, int idx) {
        if (idx == arr.length) {
            return 0;
        }
        if (dp[prev + 1][idx] != -1) {
            return dp[prev + 1][idx];
        }
        int res = (int) 1e9;
        if (arr[idx] == 1) {
            final int l = st.query1(1, idx);
            if (l != -1) {
                st.update(l, 1);
                res = Math.min(res, Math.abs(idx - l) + dfs(arr, l, idx + 1));
                st.update(l, 0);
            }
            final int r = st.query2(1, idx);
            if (r != -1) {
                st.update(r, 1);
                res = Math.min(res, Math.abs(idx - r) + dfs(arr, r, idx + 1));
                st.update(r, 0);
            }
        } else {
            res = Math.min(res, dfs(arr, prev,idx + 1));
        }
        return dp[prev + 1][idx] = res;
    }

    static final class Utils {
        private static class Shuffler {
            private static void shuffle(int[] x) {
                final Random r = new Random();

                for (int i = 0; i <= x.length - 2; i++) {
                    final int j = i + r.nextInt(x.length - i);
                    swap(x, i, j);
                }
            }

            private static void shuffle(long[] x) {
                final Random r = new Random();

                for (int i = 0; i <= x.length - 2; i++) {
                    final int j = i + r.nextInt(x.length - i);
                    swap(x, i, j);
                }
            }

            private static void swap(int[] x, int i, int j) {
                final int t = x[i];
                x[i] = x[j];
                x[j] = t;
            }

            private static void swap(long[] x, int i, int j) {
                final long t = x[i];
                x[i] = x[j];
                x[j] = t;
            }
        }

        public static void shuffleSort(int[] arr) {
            Shuffler.shuffle(arr);
            Arrays.sort(arr);
        }

        public static void shuffleSort(long[] arr) {
            Shuffler.shuffle(arr);
            Arrays.sort(arr);
        }

        private Utils() {}
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        private String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    //noinspection CallToPrintStackTrace
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int[] nextIntArray(int n) {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++) { a[i] = nextInt(); }
            return a;
        }

        long[] nextLongArray(int n) {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++) { a[i] = nextLong(); }
            return a;
        }
    }
}
