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.
/*

 █    ██  ███▄    █  ██ ▄█▀ ███▄    █  ▒█████   █     █░ ███▄    █
 ██  ▓██▒ ██ ▀█   █  ██▄█▒  ██ ▀█   █ ▒██▒  ██▒▓█░ █ ░█░ ██ ▀█   █
▓██  ▒██░▓██  ▀█ ██▒▓███▄░ ▓██  ▀█ ██▒▒██░  ██▒▒█░ █ ░█ ▓██  ▀█ ██▒
▓▓█  ░██░▓██▒  ▐▌██▒▓██ █▄ ▓██▒  ▐▌██▒▒██   ██░░█░ █ ░█ ▓██▒  ▐▌██▒
▒▒█████▓ ▒██░   ▓██░▒██▒ █▄▒██░   ▓██░░ ████▓▒░░░██▒██▓ ▒██░   ▓██░
░▒▓▒ ▒ ▒ ░ ▒░   ▒ ▒ ▒ ▒▒ ▓▒░ ▒░   ▒ ▒ ░ ▒░▒░▒░ ░ ▓░▒ ▒  ░ ▒░   ▒ ▒
░░▒░ ░ ░ ░ ░░   ░ ▒░░ ░▒ ▒░░ ░░   ░ ▒░  ░ ▒ ▒░   ▒ ░ ░  ░ ░░   ░ ▒░
 ░░░ ░ ░    ░   ░ ░ ░ ░░ ░    ░   ░ ░ ░ ░ ░ ▒    ░   ░     ░   ░ ░
   ░              ░ ░  ░            ░     ░ ░      ░             ░

*/
////////////////////////////////////////////////////////---------------DEFINE + DECLARATION-------------/////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
using namespace std;
#define BIT_ON(mask, i) (mask | (1 << i))
#define BIT_OFF(mask, i) (mask ^ (1 << i))
#define C_BITS(i) __builtin_popcount(i)
#define GET_BIT(mask, i)    ((mask >> i) & 1)
#define FOR(i, a, b) for (int i = a; i <= b; i++)
#define FORD(i, a, b) for (int i = a; i >= b; i--)
#define TASK "Armchairs"
//Sources:  https://codeforces.com/contest/1525/problem/D

int const oo = 1e9 + 7;
int a[5005], p[2552], f[2552][5005], cnt, n;

////////////////////////////////////////////////////////---------------------FUNCTION------------------/////////////////////////////////////////////////////////////////////////////

int dp(int st, int id)
{
    if (st >= cnt)  return 0;
    if (id >= n)    return oo;
    if (f[st][id] != -1)    return f[st][id];
    if (a[id])  return  f[st][id] = dp(st, id + 1);
    return f[st][id] = min(dp(st + 1, id + 1) + abs(p[st] - id), dp(st, id + 1));
}

///////////////////////////////////////////////////////------------------------MAIN--------------------/////////////////////////////////////////////////////////////////////////////

int main()
{
    if (fopen(TASK".inp", "r"))     {freopen(TASK".inp", "r", stdin);    freopen(TASK".out", "w", stdout);}
    ios_base::sync_with_stdio(0); cin.tie(); cout.tie();
    cin >> n;
    memset(f, -1, sizeof(f));
    for (int i = 0; i < n; i++) {cin >> a[i]; if (a[i]) p[cnt++] = i;}
    cout << dp(0, 0);
    return 0;
}

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
