## Problem Description

Jiahai has *N* baskets of apples, with the *i*th basket having a total of *A*_{i} apples. Since Jiahai is very neat, it is guaranteed that *A* is in non-decreasing order.

He wishes to merge a certain subset of these baskets into a larger container. He records down a sorted list of the total number of apples he will get for all possible subsets of baskets.

However, a gust of wind hit and blew all of Jiahai's baskets away (but not his paper, somehow). Help Jiahai recover his original array *A*.

## Limits

Subtask 1 (11%): 1 ≤ N ≤ 2, 0 ≤ A_{i} ≤ 10^{5}.

Subtask 2 (13%): 1 ≤ N ≤ 4, 0 ≤ A_{i} ≤ 10^{5}.

Subtask 3 (7%): 1 ≤ N ≤ 20, 0 ≤ A_{i} ≤ 1.

Subtask 4 (22%): 1 ≤ N ≤ 20, 0 ≤ A_{i} ≤ 10^{5}, there will only be at most two unique values of A_{i}.

Subtask 5 (47%): 1 ≤ N ≤ 20, 0 ≤ A_{i} ≤ 10^{5}.

Subtask 6 (0%): Sample Testcases.

## Input

The first line of input will contain one integer, *N*.

The second line of input will contain 2^{N} integers, representing the sorted list of numbers Jiahai recorded.

## Output

The output should contain *N* lines, with each line containing one integer, representing the original array *A*.

## Sample Testcase 1

### Input

3
0 1 5 6 6 7 11 12

### Output

1
5
6

## Sample Testcase 2

### Input

3
0 3 4 5 7 8 9 12

### Output

3
4
5