Fibonacci subsequence

Christopher studied sequences and permutations at school today. He really liked the Fibonacci sequence. A sequence of numbers a[1], a[2], ... is Fibonacci, if for any i > 2 it is true that a[i] = a[i-1] + a[i-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 10^9.

Output

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

Examples