List of Sums

• Time limit: 1.00 s
• Memory limit: 512 MB

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.