Score: $200$ points

问题陈述

一个由小写英文字母组成的字符串 $S$ 如果满足以下所有整数 $i$（$i$ 不小于 $1$）的属性，则称其为一个好字符串：

• 在 $S$ 中恰好有正好零个或正好两个不同的字母出现恰好 $i$ 次。

给定一个字符串 $S$，请确定它是否是一个好字符串。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

A string $S$ consisting of lowercase English letters is a good string if and only if it satisfies the following property for all integers $i$ not less than $1$:

• There are exactly zero or exactly two different letters that appear exactly $i$ times in $S$.

Given a string $S$, determine if it is a good string.

Constraints

• $S$ is a string of lowercase English letters with a length between $1$ and $100$, inclusive.

Input

The input is given from Standard Input in the following format:

$S$

Output

Print Yes if $S$ is a good string, and No otherwise.

Sample Input 1

commencement

Sample Output 1

Yes

For the string commencement, the number of different letters that appear exactly $i$ times is as follows:

• $i=1$: two letters (o and t)
• $i=2$: two letters (c and n)
• $i=3$: two letters (e and m)
• $i\geq 4$: zero letters

Therefore, commencement satisfies the condition of a good string.

Sample Input 2

banana

Sample Output 2

No

For the string banana, there is only one letter that appears exactly one time, which is b, so it does not satisfy the condition of a good string.

Sample Input 3

ab

Sample Output 3

Yes