该比赛已结束，您无法在比赛模式下递交该题目。您可以点击“在题库中打开”以普通模式查看和递交本题。

Problem Statement

A string $S$ consisting of lowercase English letters is considered a good string if and only if it satisfies the following property for all integers $i \geq 1$:

• 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 provided in the following format:

S

Output

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

Example

commencement

Yes

Explanation

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.

banana

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.

ab

Yes