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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分