Addition

There are N integers written on a blackboard. The i-th integer is A_i.

Takahashi will repeatedly perform the following operation on these numbers:

• Select a pair of integers, A_i and A_j, that have the same parity (that is, both are even or both are odd) and erase them.
• Then, write a new integer on the blackboard that is equal to the sum of those integers, A_i+A_j.

Determine whether it is possible to have only one integer on the blackboard.

Constraints

• 2 ≦ N ≦ 10^5
• 1 ≦ A_i ≦ 10^9
• A_i is an integer.

Input

The input is given from Standard Input in the following format:

N A_1 A_2 … A_N

Output

If it is possible to have only one integer on the blackboard, print YES. Otherwise, print NO.

Examples

Input

3 1 2 3

Output

YES

Input

5 1 2 3 4 5

Output

NO

inputFormat

Input

The input is given from Standard Input in the following format:

N A_1 A_2 … A_N

outputFormat

Output

If it is possible to have only one integer on the blackboard, print YES. Otherwise, print NO.

Examples

Input

3 1 2 3

Output

YES

Input

5 1 2 3 4 5

Output

NO

样例

5
1 2 3 4 5

NO