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: Runtime Error)

use std::io;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::f64::consts::PI;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

fn main() {
    let s: Vec<char> = read_line().trim().chars().collect();
    let line: Vec<i32> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let mut x = line[0];
    let y = line[1];

    let mut tmp = 0;
    let mut dir = false;
    let mut xs = Vec::new();
    let mut ys = Vec::new();
    for i in 0..s.len() {
        if s[i] == 'T' {
            if tmp > 0 {
                if dir {
                    ys.push(tmp);
                } else {
                    xs.push(tmp);
                }
                tmp = 0;
            }

            dir = !dir;
        } else {
            tmp+= 1;
        }
    }

    if tmp > 0 {
        if dir {
            ys.push(tmp);
        } else {
            xs.push(tmp);
        }
    }

    if s[0] == 'F' && xs.len() > 0 {
        x -= xs[0];
        xs.remove(0);
    }

    let mut ans = true;

    let mut table = vec![false; 8010];
    table[0] = true;
    for i in 0..xs.len() {
        let mut tmp = vec![false; 8010];
        for j in 0..table.len() {
            if table[j] {
                let n = (j as i32 - xs[i]).abs() as usize;
                tmp[n] = true;
                let n = (j as i32 + xs[i]).abs() as usize;
                tmp[n] = true;
            }
        }
        table = tmp.clone();
    }
    if (x.abs() as usize) < table.len() {
        ans &= table[x.abs() as usize];
    } else {
        ans = false;
    }
    
    let mut table = vec![false; 8010];
    table[0] = true;
    for i in 0..ys.len() {
        let mut tmp = vec![false; 8010];
        for j in 0..table.len() {
            if table[j] {
                let n = (j as i32 - ys[i]).abs() as usize;
                tmp[n] = true;
                let n = (j as i32 + ys[i]).abs() as usize;
                tmp[n] = true;
            }
        }
        table = tmp.clone();
    }
    if (y.abs() as usize) < table.len() {
        ans &= table[y.abs() as usize];
    } else {
        ans = false;
    }

    if ans {
        println!("Yes");
    } else {
        println!("No");
    }
}