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.
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<ll, ll>;
using vpii = vector<pii>;
using vint = vector<ll>;
using sint = set<ll>;
using msint = multiset<ll>;
using vb = vector<bool>;
using str = string;
const ll N = 3e5 + 5;
const ll Inf = 1e9 + 7;
const ll Mod = 998244353;
const ll inf = 1e18 + 7;
void solve() {
  ll k;
  cin >> k;
  vector<pii> a(k, {0, 0});
  for (ll i = 0; i < k; ++i) {
    cin >> a[i].first;
    a[i].second = a[i].first;
  }
  ll ans = 0;
  for (ll i = 0; i < k; ++i) {
    if (a[i].first != 1 || a[i].second != 1) {
      continue;
    }
    ll mn = Inf, mi = -1;
    for (ll j = 0; j < k; ++j) {
      if (i == j || a[j].first == 1) {
        continue;
      }
      if (mn > abs(i - j)) {
        mi = j;
        mn = abs(i - j);
        if (j > i) {
          break;
        }
      }
    }
    ans += mn;
    a[mi].first = 1;
  }
  cout << ans;
}
int32_t main() {
  ll t = 1;
  while (t--) {
    solve();
  }
}
