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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <string.h>
int main(void){
    int sa[120],ta[120] ;
    char s[120],t[120],z[30]="abcdefghijklmnopqrstuvwxyz" ;
    scanf ("%s%s",s,t) ;
    for (int i=0; i<strlen(s); i++ ){
        for (int j=0; j<30; j++ ){
            if ( s[i]==z[j] ){
                sa[i] = j ;
            }
        }
    }
    for (int i=0; i<strlen(s); i++ ){
        for (int j=i+1; j<strlen(s); j++){
            int tmp=0 ;
            if ( sa[i]>sa[j] ){
                tmp = sa[i] ;
                sa[i] = sa[j] ;
                sa[j] = tmp ;
            }
        }
    }
    for (int i=0; i<strlen(t); i++ ){
        for (int j=0; j<30; j++ ){
            if ( t[i]==z[j] ){
                ta[i] = j ;
            }
        }
    }
    for (int i=0; i<strlen(t); i++ ){
        for (int j=i+1; j<strlen(t); j++){
            int tmp=0 ;
            if ( ta[i]<ta[j] ){
                tmp = ta[i] ;
                ta[i] = ta[j] ;
                ta[j] = tmp ;
            }
        }
    }
    for (int i=strlen(s); i<120; i++){
        sa[i] = -999 ;
    }
    for (int i=strlen(t); i<120; i++){
        ta[i] = -999 ;
    }
    int cnt = 0;
    for (int i=0; i<120; i++){
        if ( sa[i]<ta[i] ){
            printf ("Yes\n") ;
            break ;
        } else if ( cnt==119 ){
            printf ("No\n") ;
            break ;
        } else {
            cnt ++ ;
        }
    }
    return 0 ;
}