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 math

n = input()
a = list(map(int,input().split()))

fr = []
oc = []

#print(a)

for i in range(len(a)):
    if a[i]==0:
        fr.append(i)
    else:
        oc.append(i)
    
if len(oc)==0:
    print(0)

else:
    inf = math.inf
    oz = len(oc)
    #print(oc)
    fz = len(fr)
    dp = [[0 for i in range(oz)] for j in range(fz)]

    for i in range(fz):
        for j in range(oz):
            dp[i][j] = inf
        
    for i in range(fz):
        dp[i][0] = abs(oc[0]-fr[i])
    
    for j in range(oz):
        prev = inf
        for i in range(j,fz):
            prev = min(prev,dp[i-1][j-1])
            dp[i][j] = min(dp[i][j],prev + abs(oc[j]-fr[i]))
    
    ans = inf

    #print(dp)

    for i in range(fz):
        ans = min(ans,dp[i][oz-1])
    
    print(ans)
    

    
