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.*;
import java.*;


class Main {
   public static void main(String[] args)
   {
      Scanner scan = new Scanner(System.in);
      String  s = scan.next();
      int     ns = 0, nt = 0;

      char[] sss = new char[s.length()];

      for(int i = 0; i < s.length(); i++){
          sss[i] = s.charAt(i);
          ns++;
          }
      Arrays.sort(sss);

      /* int Mins = sss[0];
       * for(int i = 0; i < s.length; i++){
       *    Mins = Math.min(Mins, sss[0]);
       *  }*/
      String t   = scan.next();
      char[] ttt = new char[t.length()];
      for(int j = 0; j < t.length(); j++){
          ttt[j] = t.charAt(j);
          nt++;
          }

      int array = s.length() <= t.length() ? s.length() : t.length();
      Arrays.sort(ttt);
      if(sss[0] > ttt[t.length() - 1]){
         System.out.println("No");
         }
      else if(sss[0] == ttt[t.length() - 1]){
              for(int i = 1; i < array; i++){
                  if(sss[i] < ttt[t.length() - 1 - i]){
                     System.out.println("Yes");
                     break;
                     }
                  else if(sss[i] > ttt[t.length() - 1 - i]){
                          System.out.println("No");
                          break;
                          }
                  if(s.length() < t.length()){
                     System.out.println("Yes");
                     }
                  else{
                      System.out.println("No");
                      }
                  }
              }
      else{
          System.out.println("Yes");
          }
   }
}