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 int SIZE = 4503;
struct cond {
  int r, c, layer;
  int last_dir;
  bool operator<(const cond& c) const { return layer > c.layer; }
};
int dir_r[] = {-1, 1, 0, 0};
int dir_c[] = {0, 0, -1, 1};
int rev[] = {1, 0, 3, 2};
int r_size;
int c_size;
bool maze[SIZE][SIZE];
int layer;
char buff[SIZE];
bool visit[SIZE][SIZE] = {0};
cond init;
void check_and_fix(cond& c) {
  if (c.c >= c_size || c.c < 0) {
    c.layer++;
    c.c += c_size;
    c.c %= c_size;
    c.r += r_size;
    c.r %= r_size;
    return;
  }
  if (c.r >= r_size || c.r < 0) {
    c.layer++;
    c.c += c_size;
    c.c %= c_size;
    c.r += r_size;
    c.r %= r_size;
    return;
  }
}
bool bfs() {
  cond now_cond;
  cond next_cond;
  return 0;
}
int main() {
  scanf("%d%d", &r_size, &c_size);
  for (int i = 0; i < r_size; i++) {
    scanf("%s", buff);
    for (int j = 0; j < c_size; j++) {
      if (buff[j] == '#') {
        maze[i][j] = 0;
      } else {
        if (buff[j] == 'S') {
          init.r = i + r_size;
          init.c = j + c_size;
          init.layer = 0;
          init.last_dir = -1;
        }
        maze[i][j] = 1;
      }
    }
  }
  for (int i = 0; i < r_size; i++) {
    for (int j = 0; j < c_size; j++) {
      maze[i + r_size][j] = maze[i][j];
      maze[i + r_size + r_size][j] = maze[i][j];
      maze[i + r_size + r_size + r_size][j] = maze[i][j];
      maze[i + r_size][j + c_size] = maze[i][j];
      maze[i + r_size + r_size][j + c_size] = maze[i][j];
      maze[i + r_size + r_size + r_size][j + c_size] = maze[i][j];
      maze[i + r_size][j + c_size + c_size] = maze[i][j];
      maze[i + r_size + r_size][j + c_size + c_size] = maze[i][j];
      maze[i + r_size + r_size + r_size][j + c_size + c_size] = maze[i][j];
    }
  }
  if (bfs()) {
    printf("Yes\n");
  } else {
    printf("No\n");
  }
}
