Christopher studied sequences and permutations at school today. He really liked the Fibonacci sequence. A sequence of numbers a1, a2, ... is Fibonacci, if for any i > 2 it is true that ai = ai-1 + ai-2.

In the evening Christopher came to visit Rabbit and saw a set of cards with numbers on his table. Christopher was immediately interested in the question - is it possible to compose a Fibonacci sequence from these numbers.

Input

The first line contains the number n (1 ≤ n ≤ 100) of elements in the sequence. The second line contains n positive integers less than 109.

Output

Print "YES" without quotes if the numbers can be used to form a Fibonacci sequence, otherwise print "NO".