Guess the Tree

1000ms

262144K

Description:

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.

Input:

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:

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

Sample Input:

4
1 1 1 4

Sample Output:

YES

Sample Input:

5
1 1 5 2 1

Sample Output:

NO

Informação

Provedor Codeforces

Código CF429C