Divvying Up

Interview

Time limit2sMemory limit512 MB

Summary

Given prize amounts from n contests, decide whether each total can be split among three team members so all three end with equal sums.

Level: Easy3 of 10
Topics: Math, Implementation, Array, Greedy
Solved: No attempts yet

Problem

A solid competitive programming team can rack up a lot of prize money. Knowing how strong your team is, you are certain to win a lot of contests, so you had better sit down now and check that everybody will receive the same fair distribution of winnings.

You will participate in multiple contests, and at the end of each one receive a set amount of prize money. You can distribute any amount to each of the three members of your team each time, but by the end everyone must have the same amount of total winnings.

Can you distribute the winnings such that everyone gets an equal amount by the end?

Input

One line containing the number of contests, $n$ ( $1 \le n \le 10^4$ ).
One line containing the prize purse for each contest, $w\_1 \ldots w\_n$ ( $1 \le w \le 10^5$ ).

Output

Output yes if the winnings can be distributed equally between three contestants, otherwise no.

Examples2

Example 1
Input
```
2
10 3
```
Expected output
```
no
```
Example 2
Input
```
3
9 8 7
```
Expected output
```
yes
```