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 sys import stdin, stdout
import heapq
import cProfile
from collections import Counter, defaultdict, deque
from functools import reduce
import math
import threading
import sys
import time


def get_int(): return int(stdin.readline().strip())
def get_tuple(): return map(int, stdin.readline().split())
def get_list(): return list(map(int, stdin.readline().split()))

def left_nearest_zero(i,ls):
    while i>=0:
        if ls[i]==0: return i
        i -= 1
    return float('inf')

def right_nearest_zero(i,ls,n):
    while i<n:
        if ls[i]==0: return i
        i += 1
    return float('inf')

def solve():
    n = get_int()
    ls = get_list()
    left_zero_cnt = [0]*n
    right_zero_cnt = [0]*n
    left_one_cnt = [0]*n
    right_one_cnt = [0]*n

    cnt_zero,cnt_one = 0,0
    for i,val in enumerate(ls):
        left_zero_cnt[i] = cnt_zero
        left_one_cnt[i] = cnt_one
        if val==0:
            cnt_zero += 1
        else:
            cnt_one += 1


    cnt_zero, cnt_one = 0, 0
    for i in range(n-1,-1,-1):
        val = ls[i]
        right_zero_cnt[i] = cnt_zero
        right_one_cnt[i] = cnt_one
        if val == 0:
            cnt_zero += 1
        else:
            cnt_one += 1

    ans = 0
    for i,v in enumerate(ls):
        if v==1:
            left_nearest = left_nearest_zero(i,ls)
            right_nearest = right_nearest_zero(i,ls,n)
            left,right =abs(left_nearest-i),abs(right_nearest-i)
            if left<=right and left_one_cnt[i]<left_zero_cnt[i]:
                ans += left
                ls[left_nearest] = 2
            elif right_one_cnt[i]>=right_zero_cnt[i] and left_one_cnt[i]<left_zero_cnt[i]:
                ans += left
                ls[left_nearest] = 2
            else:
                ans += right
                ls[right_nearest] = 2
    print(ans)


testcases = False
if testcases:
    t = get_int()
    for _ in range(t):
        solve()
else:
    solve()
