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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Iterator;
import java.util.Collections;
import java.util.Comparator;
import java.util.Random;
import java.util.Map;
import java.util.HashMap;
 
class Main{
        public static void main(String args[]){
                Scanner sc = new Scanner(System.in);
                String s = sc.next();
                String t = sc.next();
                ArrayList<Character> S = new ArrayList<Character>();
                for(int i=0; i<s.length(); i++){
                    S.add(s.charAt(i));
                }
                ArrayList<Character> T = new ArrayList<Character>();
                for(int i=0; i<t.length(); i++){
                    T.add(t.charAt(i));
                }
                Collections.sort(S,Collections.reverseOrder());
                Collections.sort(T);
                
                boolean ch = true;
                boolean same = true;
                for(int i=0; i<Math.min(S.size(),T.size()); i++){
                    if(S.get(i)==T.get(i)){
                        same = true;
                        ch = true;
                    }else if(S.get(i)<T.get(i)){
                        same = false;
                        ch = true;
                    }
                    else{
                        same = false;
                        ch = false;
                        break;
                    }
                }
                
                if(ch && !same){
                    System.out.println("Yes");
                }else if(ch && same){
                    if(S.size()<T.size()){
                        System.out.println("Yes");
                    }else{
                        System.out.println("No");
                    }
                }else if(!ch){
                    System.out.println("No");
                }
        }
}