Piggy Bank

Limits: 2 sec., 256 MiB

Kerem and Asli have just broken their piggy bank. Now they have \(N\) coins, each of which is either 1-lira or 2-lira coins. Don’t ask where they got 2-lira coins from, that’s a secret.

Can you tell if it’s possible to divide the coins between Kerem and Asli so that they receive an equal total amount?

Input

The first line contains a single integer number \(N\) — the number of coins. The next line contains \(N\) integer numbers — the values of coins they have. Each of the numbers is either 1 or 2, representing 1-lira and 2-lira coins, respectively.

Output

Output string YES if it’s possible to divide the coins properly, and NO otherwise.

Constraints

\(1 \le N \le 100000\).

Samples

Input (stdin)	Output (stdout)
7 2 2 2 1 1 1 1	YES

Input (stdin)	Output (stdout)
4 2 1 1 1	NO

Notes

One of possible divisions for the first sample is \((2, 2, 1)\) and \((2, 1, 1, 1)\).

Element Type	Created	Who	Problem	Compiler	Result	Time (sec.)	Memory (MiB)	#	Actions