A9564 | Guess the Tree

Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food.

Iahub asks Iahubina: can you build a rooted tree, such that

- each internal node (a node with at least one son) has at least two sons;
- node $i$ has $c_{i}$ nodes in its subtree?

Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain $n$ nodes.

The first line of the input contains integer $n$ ( $1<=n<=24$ ). Next line contains $n$ positive integers: the $i$ -th number represents $c_{i}$ $(1<=c_{i}<=n)$ .

Output on the first line "YES" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output "NO" (without quotes).