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.
# from collections import defaultdict
from sys import stdin
input = stdin.readline

N = int(input())

arr = list(map(int, input().split()))
visit = [False] * N
ocu = 0
free = 0
for i in range(N):
    if arr[i] == 1:
        visit[i] = True
        ocu += 1
    else:
        free += 1

res = 0
before_0 = 0
for i in range(N):
    if visit[i] == False:
        before_0 += 1
        continue
    if visit[i] and arr[i] != 1:
        continue

    if arr[i] == 1:
        if before_0 == 0:
            cnt = 0
            for j in range(i+1, N):
                cnt += 1
                if visit[j] == False:
                    free -= 1
                    ocu -= 1
                    visit[j] = True
                    res += cnt
                    break
        elif ocu - (free - before_0) <= 0:
            cnt = 0
            for j in range(1, max(N - i, i + 1)):
                cnt += 1
                if 0 <= i - j:
                    if visit[j] == False:
                        free -= 1
                        ocu -= 1
                        before_0 -= 1
                        visit[j] = True
                        res += cnt
                        break
                elif i + j < N:
                    if visit[j] == False:
                        free -= 1
                        ocu -= 1
                        visit[j] = True
                        res += cnt
                        break
        else:
            tmp = (free - before_0) - ocu
            cnt = 0
            for j in range(i-1, -1, -1):
                cnt += 1
                if visit[j] == False and tmp == 1:
                    free -= 1
                    ocu -= 1
                    before_0 -= 1
                    visit[j] = True
                    res += cnt
                    break
                elif visit[j] == False:
                    tmp -= 1

print(res)
