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.*;


public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        String a = sc.next();
        String b = sc.next();

        ArrayList<Character> anagramA = new ArrayList<Character>();
        for(int i = 0; i < a.length(); i++){
            char c = a.charAt(i);
            int insertIndex = anagramA.size();
            for(int j = 0; j < anagramA.size(); j++){
                if(insertIndex == anagramA.size() && c <= anagramA.get(j)){
                    insertIndex = j;
                }
            }
            anagramA.add(insertIndex, c);
        }
        ArrayList<Character> anagramB = new ArrayList<Character>();
        for(int i = 0; i < b.length(); i++){
            char c = b.charAt(i);
            int insertIndex = anagramB.size();
            for(int j = 0; j < anagramB.size(); j++){
                if(insertIndex == anagramB.size() && c >= anagramB.get(j)){
                    insertIndex = j;
                }
            }
            anagramB.add(insertIndex, c);
        }

        String ans = "No";

        for(int i = 0; i < Math.min(anagramA.size(), anagramB.size()); i++){
            if(anagramA.get(i) < anagramB.get(i)){
                ans = "Yes";
                break;
            }else if(i < Math.min(anagramA.size(), anagramB.size())-1){
                break;
            }else if(i == Math.min(anagramA.size(), anagramB.size())-1 && anagramA.size() < anagramB.size()){
                ans = "Yes";
            }
        }
        System.out.println(ans);
    }
}