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: Accepted)

use std::io::stdin;

fn read() -> String {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}

use std::cmp::Ordering::{Equal, Greater, Less};
fn main() {
    let mut s: Vec<char> = read().chars().collect();
    let mut t: Vec<char> = read().chars().collect();
    s.sort();
    t.sort_by(|l, r| r.cmp(&l));
    let ans = s
        .iter()
        .zip(t.iter())
        .fold(Equal, |ans, (s, t)| match (ans, s.cmp(&t)) {
            (Equal, Equal) => Equal,
            (Equal, Less) | (Less, _) => Less,
            _ => Greater,
        });
    println!(
        "{}",
        match ans {
            Equal if s.len() < t.len() => "Yes",
            Less => "Yes",
            _ => "No",
        }
    );
}