CodeForces-1201B (思维题)

题目：

You are given an array a1,a2,…,ana1,a2,…,an.

In one operation you can choose two elements aiai and ajaj (i≠ji≠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 nn (2≤n≤1052≤n≤105) — the size of the array.

The second line contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤1091≤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 33 operations:

• Decrease a1a1 and a2a2,
• Decrease a3a3 and a4a4,
• Decrease a3a3 and a4a4

In the second example, one can show that it is impossible to make all elements equal to zero.

 

思路：因为是成对成对的减少，所以总数首先是偶数。其次还要满足最大的数小于等于总数的一半，这样才能保证最大的数消去(类似于鸽巢原理)。

AC代码：

#include
#include
#include
#include
#include
#include