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.
# Problem: D. Armchairs
# Contest: Codeforces - Educational Codeforces Round 109 (Rated for Div. 2)
# URL: https://codeforces.com/contest/1525/problem/D
# Memory Limit: 512 MB
# Time Limit: 2000 ms
# 
# KAPOOR'S

from sys import stdin, stdout 

def INI():
	return int(stdin.readline())
	
def INL():
	return [int(_) for _ in stdin.readline().split()]
	
def INS():
	return stdin.readline()

def MOD():
    return pow(10,9)+7
	
def OPS(ans):
	stdout.write(str(ans)+"\n")
	
def OPL(ans):
	[stdout.write(str(_)+" ") for _ in ans]
	stdout.write("\n")

from queue import LifoQueue
	
def fun():	
	A=LifoQueue()
	B=LifoQueue()
	ans=[]
	# print(X)
	for _ in range(n):
		if X[_]==0:
			if not B.empty():
				x=B.get()
				ans.append(_-x)
			else:
				A.put(_)
		else:
			if not A.empty():
				x=A.get()
				ans.append(_-x)
			else:
				B.put(_)
	return ans
	
if __name__=="__main__":
	n=INI()
	X=INL()
	
	ans1=fun()
	X=X[::-1]
	ans2=fun()
	ans=0
	for _,__ in zip(ans1,ans2):
		ans+=min(_,__)
	OPS(ans)