The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.

The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.

One move is choosing an integer i (1 ≤ i ≤ n) such that ai > 0 and an integer t (t ≥ 0) such that i + 2t ≤ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).

You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 ≤ k < n).

Input

The first input line contains a single integer n. The second line contains n integers ai (0 ≤ ai ≤ 104), separated by single spaces.

The input limitations for getting 20 points are: 

  * 1 ≤ n ≤ 300



The input limitations for getting 50 points are: 

  * 1 ≤ n ≤ 2000



The input limitations for getting 100 points are: 

  * 1 ≤ n ≤ 105

Output

Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams, or the %I64d specifier.

Examples

Input

4
1 0 1 2


Output

1
1
3


Input

8
1 2 3 4 5 6 7 8


Output

1
3
6
10
16
24
40
#include <bits/stdc++.h>
using namespace std;
const long long int mod = 1e9 + 7;
const long double error = 2e-6;
const long double PI = acosl(-1);
inline long long int MOD(long long int x, long long int m = mod) {
  long long int y = x % m;
  return (y >= 0) ? y : y + m;
}
const int inf = 1e9;
const long long int infl = 1061109567;
const int nmax = 1000 + 10;
int main() {
  int t;
  cin >> t;
  for (int kk = 1; kk <= t; kk++) {
    int n;
    cin >> n;
    int i;
    std::vector<int> v1(n);
    std::vector<int> alada;
    for (i = 0; i < n; i++) {
      int xx;
      cin >> xx;
      v1[i] = xx;
      if (i == 0) {
        alada.push_back(xx);
      } else {
        if (v1[i - 1] != xx) alada.push_back(xx);
      }
    }
    if (n == 1 or n == 2 or alada.size() == 1) {
      cout << 0 << endl;
      continue;
    }
    if (kk != kk) {
      cout << v1[0];
      cout << v1[1];
      cout << v1[2];
      cout << v1[3];
      cout << v1[4];
      cout << v1[5];
      cout << v1[6];
      cout << v1[7];
      cout << v1[8];
      cout << v1[9];
      cout << endl;
      continue;
    }
    int cn = 2;
    int bort_alada = 1;
    for (i = n - 2; i > 0; i--) {
      if (v1[i] == v1[i - 1] && v1[i] == v1[i + 1]) {
        cn++;
        continue;
      } else if (v1[i] == v1[i + 1] && v1[i] != v1[i - 1]) {
        int suck = alada.size() - (bort_alada - 1 - 1) - 1;
        if (suck < 0 or suck >= alada.size()) {
          cn++;
        } else {
          if (v1[i] > alada[suck] or v1[i] > v1[i - 1]) {
            cn++;
          } else {
            break;
          }
        }
        continue;
      } else if (v1[i] != v1[i + 1] && v1[i] == v1[i - 1]) {
        bort_alada++;
        cn++;
        continue;
      } else if (v1[i] != v1[i - 1] && v1[i] != v1[i + 1]) {
        bort_alada++;
        if (v1[i] > v1[i - 1] or v1[i] > v1[i + 1]) {
          cn++;
        } else {
          break;
        }
        continue;
      }
    }
    cout << n - cn << endl;
  }
  return 0;
}
