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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io;
use std::collections::HashSet;

fn main() {
	let mut buf = String::new();
	io::stdin().read_line(&mut buf).expect("");
	let s:Vec<char> = buf.trim().chars().collect();
	let mut buf = String::new();
	io::stdin().read_line(&mut buf).expect("");
	let t:Vec<char> = buf.trim().chars().collect();
	
	let mut sind = HashSet::new();
	let mut tind = HashSet::new();
	for i in 0..s.len() {
		for j in 0..t.len() {
			if s[i] == t[j] {
				if tind.insert(j) {
					sind.insert(i);
					break;
				}
			}
		}
	}
	let mut s2:Vec<char> = Vec::new();
	let mut t2:Vec<char> = Vec::new();
	for i in 0..s.len() {
		if sind.insert(i) {
			s2.push(s[i]);
		}
	}
	for i in 0..t.len() {
		if tind.insert(i) {
			t2.push(t[i]);
		}
	}
	
	if s2.len() == 0 && t2.len() != 0 {
		println!("Yes");
	}else if s2.len() != 0 && t2.len() == 0 {
		println!("No");
	}else if s2.len() == 0 && t2.len() == 0 {
		println!("No");
	}else{
		s2.sort();
		t2.sort();
		if s2[0] < t2[t2.len() - 1] {
			println!("Yes");
		}else{
			println!("No");
		}
	}
}