Two Anagrams

You are given strings s and t, consisting of lowercase English letters. You will create a string s' by freely rearranging the characters in s. You will also create a string t' by freely rearranging the characters in t. Determine whether it is possible to satisfy s' < t' for the lexicographic order.

Constraints

• The lengths of s and t are between 1 and 100 (inclusive).
• s and t consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s t

Output

If it is possible to satisfy s' < t', print Yes; if it is not, print No.

Examples

Input

yx axy

Output

Yes

Input

ratcode atlas

Output

Yes

Input

cd abc

Output

No

Input

w ww

Output

Yes

Input

zzz zzz

Output

No

inputFormat

Input

Input is given from Standard Input in the following format:

s t

outputFormat

Output

If it is possible to satisfy s' < t', print Yes; if it is not, print No.

Examples

Input

yx axy

Output

Yes

Input

ratcode atlas

Output

Yes

Input

cd abc

Output

No

Input

w ww

Output

Yes

Input

zzz zzz

Output

No

样例

ratcode
atlas

Yes