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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use v5.18;
use warnings;
use utf8;
use Data::Dumper;
use List::Util qw( sum );
use Test::More;

sub line { chomp(my $str = <>); $str; }
sub split_line { (split / /, line) }

main();

sub main {
  my ($str1, $str2) = split_line;
  say solve($str1, $str2) ? 'Yes' : 'No';
}

sub ord_sum_sort_small {
  my ($str, $len) = @_;
  my @ords = ( sort { $a <=> $b } map { ord $_ } split //, $str )[0 .. $len - 1];
  sum @ords;
}

sub ord_sum_sort_big {
  my ($str, $len) = @_;
  my @ords = ( sort { $b <=> $a } map { ord $_ } split //, $str )[0 .. $len - 1];
  sum @ords;
}

sub solve {
  my ($str1, $str2) = @_;
  my $len = length($str1) < length($str2) ? length($str1) : length($str2);
  my $s1_ord_sum = ord_sum_sort_small($str1, $len);
  my $s2_ord_sum = ord_sum_sort_big($str2, $len);
  if ($s1_ord_sum < $s2_ord_sum) {
    1;
  }
  elsif ($s1_ord_sum == $s2_ord_sum) {
    length $str1 < length $str2;
  }
  else {
    0;
  }
}