Score : $200$ points

Problem Statement

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.

Notes

For a string $a = a_1 a_2 ... a_N$ of length $N$ and a string $b = b_1 b_2 ... b_M$ of length $M$, we say $a < b$ for the lexicographic order if either one of the following two conditions holds true:

• $N < M$ and $a_1 = b_1$, $a_2 = b_2$, ..., $a_N = b_N$.
• There exists $i$ ($1 \leq i \leq N, M$) such that $a_1 = b_1$, $a_2 = b_2$, ..., $a_{i - 1} = b_{i - 1}$ and $a_i < b_i$. Here, letters are compared using alphabetical order.

For example, xy $<$ xya and atcoder $<$ atlas.

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.

yx
axy

Yes

We can, for example, rearrange yx into xy and axy into yxa. Then, xy $<$ yxa.

ratcode
atlas

Yes

We can, for example, rearrange ratcode into acdeort and atlas into tslaa. Then, acdeort $<$ tslaa.

cd
abc

No

No matter how we rearrange cd and abc, we cannot achieve our objective.

w
ww

Yes

zzz
zzz

No