Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A2. Educational Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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 *a*_{i} numbered from 1 to *n*. The goal of the game is to make numbers *a*_{1}, *a*_{2}, ..., *a*_{k} (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 *a*_{i} > 0 and an integer *t* (*t* ≥ 0) such that *i* + 2^{t} ≤ *n*. After the values of *i* and *t* have been selected, the value of *a*_{i} is decreased by 1, and the value of *a*_{i + 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 *a*_{i}. 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 *a*_{i} (0 ≤ *a*_{i} ≤ 10^{4}), 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*≤ 10^{5}

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 *a*_{i} 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

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/22/2017 03:45:06 (c4).

Desktop version, switch to mobile version.

User lists

Name |
---|