CF429C.Guess the Tree

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

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.

输入格式

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

输出格式

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

输入输出样例

输入#1
```
4
1 1 1 4
```
输出#1
```
YES
```
输入#2
```
5
1 1 5 2 1
```
输出#2
```
NO
```

首页