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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(input){
  input = input.split("\n");
  var s = input[0].split('');
  var t = input[1].split('');
  s.sort((a,b)=>a>b);
  t.sort((a,b)=>a<b);
  if(s[0]<t[0]){
    console.log('Yes');
  }else if(s[0]==t[0]){
    evenCheck(1);
  }else{
    console.log('No');
  }
  function evenCheck(n){
    if(s[n]<t[n]){
      console.log('Yes');
      return;
    }else if(s[n]>t[n]){
      console.log('No');
      return;
    }
    if((s.length==n)&&(t.length==n)){
      console.log('No');
      return;
    }else if(s.length==n){
      if(s.length<t.length){
        console.log('Yes');
        return;
      }
    }else if(t.length==n){
      if(s.length>t.length){
        console.log('No');
        return;
      }
    }
    if(s[n]==t[n]){
      n++;
      return evenCheck(n);
    }
  }
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));