List of Sums

List A consists of n positive integers, and list B contains the sum of each element pair of list A. For example, if A=[1,2,3], then B=[3,4,5], and if A=[1,3,3,3], then B=[4,4,4,6,6,6]. Given list B, your task is to reconstruct list A.

Input

The first input line has an integer n: the size of list A. The next line has \frac{n(n-1)}{2} integers: the contents of list B. You can assume that there is a list A that corresponds to the input, and each value in A is between 1 \dots k.

Output

Print n integers: the contents of list A. You can print the values in any order. If there are more than one solution, you can print any of them.

Constraints

$3 \le n \le 100$

$1 \le k \le 10^9$

Example

Input

4
4 4 4 6 6 6

Output

1 3 3 3

Explanation: In this case list A can be either [1,3,3,3] or [2,2,2,4] and both solutions are accepted.