Problem2812--Guess the Tree

2812: Guess the Tree

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ci 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 ci (1≤ci≤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).

Examples
Input
4
1 1 1 4
Output
YES
Input
5
1 1 5 2 1
Output
NO

Source/Category

 
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