Problem:
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.

Sample Input 1

yx
axy

Sample Output 1

Yes

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

Sample Input 2

ratcode
atlas

Sample Output 2

Yes

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

Sample Input 3

cd
abc

Sample Output 3

No

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

Sample Input 4

w
ww

Sample Output 4

Yes

Sample Input 5

zzz
zzz

Sample Output 5

No

Solution in PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$f = fopen( 'php://stdin', 'r' );
$line1 = fgets($f);
$line2 = fgets($f);

$stringParts1 = str_split($line1);
sort($stringParts1);
$count_pre1 = count($stringParts1);
$stringParts1 = array_unique($stringParts1);
$count_post1 = count($stringParts1);

$stringParts2 = str_split($line2);
sort($stringParts2);
$count_pre2 = count($stringParts2);
$stringParts2 = array_unique($stringParts2);
$count_post2 = count($stringParts2);


if ($stringParts1[0] > end($stringParts2)) {
    echo('No');
    exit();
} elseif ($stringParts1[0] === $stringParts2[-1]) {
    if ($count_post1 === 1 && $count_post2 === 1 && $count_pre1 < $count_pre2) {
        echo('Yes');
    } else {
        echo('No');
    }
    exit();
} else {
    echo('Yes');
}