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
input = stdin.readline
# import io,os
# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
def im():
    return map(int,input().split())
def ii():
    return int(input())
def il():
    return list(map(int,input().split()))
def ins():
    return input()[:-1]

def check(lis):    
    for i in range(1,len(lis)):
        if lis[i]<=lis[i-1]:
            return False
    return True
 
n = ii()
lis = il()
ans=0
for i in range(n):
    if lis[i]==1:
        l = i-1
        r = i+1
        while l>=0 and lis[l]!=0:
            l-=1
        while r<n and lis[r]!=0:
            r+=1
        if l==-1:
            ans+=r-i
            lis[r] = 2
        elif r==n:
            ans+=i-l
            lis[l] = 2
        else:
            if i-l<=r-i:
                ans+=i-l
                lis[l] = 2
            else:
                ans+=r-i
                lis[r] = 2
        # print(lis)
print(ans)
