Background

Description

Given an array of ints, is it possible to divide the ints into two groups, so that the sum of the two groups is the same, with these constraints: all the values that are multiple of 5 must be in one group, and all the values that are a multiple of 3 (and not a multiple of 5) must be in the other. (No loops needed.)

Format

Input

Output

Samples

[1 1]

true

[1 1 1]

false

[2 4 2]

true

Limitation

1s, 1024KiB for each test case.