CSES - List of Sums
  • Time limit: 1.00 s
  • Memory limit: 512 MB

List AA consists of nn positive integers, and list BB contains the sum of each element pair of list AA.

For example, if A=[1,2,3]A=[1,2,3], then B=[3,4,5]B=[3,4,5], and if A=[1,3,3,3]A=[1,3,3,3], then B=[4,4,4,6,6,6]B=[4,4,4,6,6,6].

Given list BB, your task is to reconstruct list AA.

Input

The first input line has an integer nn: the size of list AA.

The next line has n(n1)2\frac{n(n-1)}{2} integers: the contents of list BB.

You can assume that there is a list AA that corresponds to the input, and each value in AA is between 1k1 \dots k.

Output

Print nn integers: the contents of list AA.

You can print the values in any order. If there are more than one solution, you can print any of them.

Constraints

  • 3n1003 \le n \le 100
  • 1k1091 \le k \le 10^9

Example

Input:

4
4 4 4 6 6 6

Output:

1 3 3 3

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