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.
'''t = int(input())
for i in range(t):
    n,m = map(int,input().split())
    x = list(map(int,input().split()))
    drn = list(map(int,input().split()))
    '''
    
n = int(input())
a = list(map(int,input().split()))
w = []
for j in range(n):
    if(a[j]==0):
        w.append(j)
#cnt=0
ans=0
for j in range(n):
    if(a[j]==1):
        mn = n+0
        ind=-1
        for k in range(len(w)):
            if(abs(w[k]-j)<mn and w[k]!=-2):
                mn = abs(w[k]-j)
                ind = k
        #print(mn)
        ans+=mn
        w[ind]=-2

ans1=0        
for j in range(n-1,-1,-1):
    if(a[j]==1):
        mn = n+0
        ind=-1
        for k in range(len(w)):
            if(abs(w[k]-j)<mn and w[k]!=-2):
                mn = abs(w[k]-j)
                ind = k
        #print(mn)
        ans1+=mn
        w[ind]=-2
print(min(ans,ans1))
    