#### Registered Users Only

Please login to utilize this feature.

Do note that this website only supports submissions in C++.

## 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

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 11 | 20 | 1s | 256MB | Minimum |

2 | 13 | 42 | 1s | 256MB | Minimum |

3 | 7 | 20 | 1s | 256MB | Minimum |

4 | 22 | 40 | 1s | 256MB | Minimum |

5 | 47 | 102 | 1s | 256MB | Minimum |

6 | 0 | 2 | 1s | 256MB | Minimum |

### Judge Compile Command

g++ ans.cpp -o stesbus -Wall -static -O2 -lm -m64 -s -w -std=gnu++14 -fmax-errors=512