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 os
import sys
from io import BytesIO, IOBase

_print = print
BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode('ascii'))
        self.read = lambda: self.buffer.read().decode('ascii')
        self.readline = lambda: self.buffer.readline().decode('ascii')


def inp():
    return sys.stdin.readline().rstrip()


def mpint():
    return map(int, inp().split(' '))


def itg():
    return int(inp())


# ############################## import
# ############################## main
def main():
    # from left person to right person
    # go to their nearest valid seat
    n = itg()
    arr = list(mpint())
    tmp = arr.copy()
    zero_idx = []
    one_idx = []
    for i, a in enumerate(arr):
        if a:
            one_idx.append(i)
        else:
            zero_idx.append(i)
    move_left_cost = []
    step = 0
    for oi, zi in zip(one_idx, zero_idx):
        # one to zero
        step += abs(oi - zi)
        move_left_cost.append(step)

    ans = lb = one = 0
    for i in range(n):
        if arr[i] != 1:
            continue
        one += 1
        arr[i] = 2
        # go left
        j = i
        step = 0
        while lb < j:
            step += 1
            j -= 1
            if not arr[j]:
                break
        l_step = n if arr[j] else step
        l_pos = j
        # go right
        j = i
        step = 0
        while j < n - 1:
            step += 1
            j += 1
            if not arr[j]:
                break
        if not arr[j] and step < l_step:
            # should go right
            ans += step
            arr[j] = 2
        else:
            ans += l_step
            arr[l_pos] = 2

        if move_left_cost[one - 1] < ans:
            ans = move_left_cost[one - 1]
            arr = tmp.copy()
            c = 0
            for j in range(n):
                if not arr[j]:
                    arr[j] = 2
                    c += 1
                if c == one:
                    break
    print(ans)


DEBUG = 0
URL = 'https://codeforces.com/contest/1525/problem/D'

if __name__ == '__main__':
    # 0: normal, 1: runner, 2: debug, 3: interactive
    if DEBUG == 1:
        import requests
        from ACgenerator.Y_Test_Case_Runner import TestCaseRunner

        runner = TestCaseRunner(main, URL)
        inp = runner.input_stream
        print = runner.output_stream
        runner.checking()
    else:
        if DEBUG != 2:
            sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
        if DEBUG:
            def print(*args, **kwargs):
                _print(*args, **kwargs)
                sys.stdout.flush()
        main()
# Please check!
