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.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String s = sc.nextLine();
		String t = sc.nextLine();

		int sNumber = s.length();
		int tNumber = t.length();

		List<String> sList = new ArrayList<>();
		List<String> tList = new ArrayList<>();

		String[] sAllay = s.split("");
		String[] tAllay = t.split("");
		for (String ss : sAllay) {
			sList.add(ss);
		}
		for (String tt : tAllay) {
			tList.add(tt);
		}

		Collections.sort(sList);
		Collections.sort(tList, Comparator.reverseOrder());
		System.out.println(sList);
		System.out.println(tList);

		String yn = null;
		int index = 0;
		int difference = sNumber - tNumber;
		if (difference < 0) {
			index = sNumber - 1;
			yn = "YES";

		} else if (difference >= 0) {
			index = tNumber - 1;
			yn = "NO";
		}

		for (int index1 = 0; index1 <= index; index1++) {
			for (int index2 = 0; index2 <= index; index2++) {
				if (index1 == index2) {
					String x = sList.get(index1);
					String y = tList.get(index2);
					int n = x.compareTo(y);
					if (n == 0) {
						break;
					} else if (n > 0) {
						System.out.println("NO");
						return;
					} else if (n < 0) {
						System.out.println("YES");
						return;
					}
				}
			}
		}
		System.out.println(yn);
	}
}