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 javax.xml.crypto.dsig.spec.ExcC14NParameterSpec;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;

public class Solution {
  private static int readInt() throws Exception {
    return Integer.parseInt(br.readLine());
  }

  private static long readLong() throws Exception {
    return Long.parseLong(br.readLine());
  }

  public static int[] readIntArray() throws Exception {
    String line = br.readLine();
    if (line == null || line.isEmpty()) return null;
    String[] lines = line.split(" ");
    int n = Integer.parseInt(lines[0]);
    int[] nums = new int[n];
    for (int i = 0; i < n; i++)
      nums[i] = Integer.parseInt(lines[i + 1]);
    return nums;
  }

  public static int[] readIntArray(int n) throws Exception {
    int[] nums = new int[n];
    String[] lines = br.readLine().split(" ");
    for (int i = 0; i < n; i++)
      nums[i] = Integer.parseInt(lines[i]);
    return nums;
  }

  public static long[] readLongArray(int n) throws Exception {
    long[] nums = new long[n];
    String[] lines = br.readLine().split(" ");
    for (int i = 0; i < n; i++)
      nums[i] = Long.parseLong(lines[i]);
    return nums;
  }

  public static String[] readStringArray(int n) throws Exception {
    String[] nums = new String[n];
    for (int i = 0; i < n; i++)
      nums[i] = br.readLine();
    return nums;
  }

  public static void printArrayInline(int[] nums) throws Exception {
    for (int i = 0; i < nums.length - 1; i++) {
      bw.write(nums[i] + " ");
    }
    bw.write(nums[nums.length - 1] + "\n");
  }

  public static void printArrayInline(long[] nums) throws Exception {
    for (int i = 0; i < nums.length - 1; i++) {
      bw.write(nums[i] + " ");
    }
    bw.write(nums[nums.length - 1] + "\n");
  }

  public static <T> void printListInLine(List<T> nums) throws Exception {
    for (int i = 0; i < nums.size() - 1; i++) {
      bw.write(nums.get(i).toString() + " ");
    }
    bw.write(nums.get(nums.size() - 1) + "\n");
  }

  public static <T> void printListMultiLine(List<T> nums) throws Exception {
    for (T num : nums) {
      bw.write(num.toString() + "\n");
    }
  }

  public static void printArrayMultiLine(int[] nums) throws Exception {
    for (int num : nums) {
      bw.write(num + "\n");
    }
  }

  public static int[] makeRandomArray(int size, int lower, int upper) {
    Random random = new Random(System.currentTimeMillis());
    int[] nums = new int[size];
    for (int i = 0; i < size; i++)
      nums[i] = random.nextInt(upper - lower + 1) + lower;
    return nums;
  }

  static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  static PrintWriter bw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
//  static {
//    try {
//      String env = System.getProperty("env-jay");
//      if (env != null && env.equals("jay")) {
//        br = new BufferedReader(new FileReader("src/input.txt"));
//        bw = new PrintWriter(new BufferedWriter(new FileWriter("src/output.txt", false)));
//      }
//    } catch (Exception e) {
//
//    }
//  }
//
//
//  private static void test() throws Exception {
//    try {
//      String env = System.getProperty("env-jay");
//      if (env != null && env.equals("jay")) {
//        var output = new BufferedReader(new FileReader("src/output.txt"));
//        var expected = new BufferedReader(new FileReader("src/expected.txt"));
//        String ans;
//        int line = 0;
//        while ((ans = expected.readLine()) != null && !ans.isEmpty()) {
//          line++;
//          String guess = output.readLine();
//          if (guess == null || guess.isEmpty()) {
//            System.err.println(String.format(
//                    "Line[%d] There is no guess.\nAnswer:[%s]"
//                    , line, ans));
//            System.exit(-1);
//          }
//          if (!ans.equals(guess)) {
//            System.err.println(String.format(
//                    "Line[%d], Wrong guess.\nAnswer:[%s]\nGuess:[%s]"
//                    , line, ans, guess));
//            System.exit(-2);
//          }
//        }
//      }
//    } catch (Exception e) {
//
//    }
//  }

  public static void main(String[] args) throws Exception {
    int testCases = 1;
    for (int iter = 1; iter <= testCases; iter++) {
      int n = readInt();
      int[] nums = readIntArray(n);
      bw.printf("%d\n", solve(nums));
    }
    bw.flush();
    bw.close();
    br.close();
    //test();
  }

  private static long solve(int[] nums) {
    int n = nums.length;
    TreeSet<Integer> free = new TreeSet<>();
    Stack<Integer> numsToMove = new Stack<>();
    long cost = 0;
    for(int i = 0; i < n; i ++) {
      if(nums[i] > 0) {
        numsToMove.push(i);
      } else {
        free.add(i);
      }
    }
    while(!numsToMove.isEmpty()) {
      int index = numsToMove.pop();
      var leftSet = free.headSet(index);
      var rightSet = free.tailSet(index);
      if(numsToMove.size() >= leftSet.size()) {
        int right = rightSet.first();
        cost += Math.abs(right - index);
        free.remove(right);
      } else {
        int left = leftSet.last();
        cost += Math.abs(left - index);
        free.remove(left);
      }
    }
    return cost;
  }
}