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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
int main() {
  string s,t;
  map<char,int> smap;
  map<char,int> tmap;
  cin >> s >> t;
  for(int i=0;i<s.size();i++){
    smap[s.at(i)]++;
  }
  for(int i=0;i<t.size();i++){
    tmap[t.at(i)]++;
  }
  if(s.size()<t.size()){
    int i=1;
    for(auto x:smap){
      if(x.second>tmap[x.first])continue;
      else if(i==smap.size()) {
        cout << "Yes" << endl;
        return 0;
      }
      i++;
    }
  }
  int count=0,same=0,n=smap.size();
  char p='z',q='a';
  for(char i='a';i<='z';i++){
    if(0<smap[i]){
      if(0<tmap[i]){
        count++;
        if(smap[i]==tmap[i]){
          same+=smap[i];
          if(2<same)same=-1000;
        }
        if(smap[i]<tmap[i]){
          if(1<count){
            //cout << i << endl;
            //cout << "Yes" << endl;
            return 0;
          }
          count++;
          q=max(q,i);
        }else if(smap[i]>tmap[i]) p=min(p,i);
      }else p=min(p,i);
    }
    if(0<tmap[i]) q=max(q,i);
    if(p<q&&0<count||same<0&&n!=1){
      //cout << p << " " << q << " " << count << " " << same << endl;
      cout << "Yes" << endl;
      return 0;
    }
  }
  //cout << p << " " << q << " " << count << " " << same << endl; 
  cout << "No" << endl;
  return 0;
}