Zero Array CodeForces - 1201B

B. Zero Array

You are given an array a1,a2,…,an.

In one operation you can choose two elements ai and aj (i≠j) and decrease each of them by one.

You need to check whether it is possible to make all the elements equal to zero or not.

Input
The first line contains a single integer n (2≤n≤105) — the size of the array.

The second line contains n integers a1,a2,…,an (1≤ai≤109) — the elements of the array.

Output
Print “YES” if it is possible to make all elements zero, otherwise print “NO”.

Examples

input
4
1 1 2 2

output
YES

input
6
1 2 3 4 5 6

output
NO

Note
In the first example, you can make all elements equal to zero in 3 operations:

Decrease a1 and a2,
Decrease a3 and a4,
Decrease a3 and a4
In the second example, one can show that it is impossible to make all elements equal to zero.

一道简单的思路题：