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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define rep(i,f,n) for(ll i=(f); (i) < (n); i++)
#define repe(i,f,n) for(ll i=(f); (i) <= (n); i++)
using namespace std;
using ll = long long;
#define MOD (ll)1000000007
#define PI 3.14159265359
#define debug(x) cout<<#x<<" :: "<<x<<"\n";
#define debug2(x,y) cout<<#x<<" :: "<<x<<"\t"<<#y<<" :: "<<y<<"\n";
#define debug3(x,y,z) cout<<#x<<" :: "<<x<<"\t"<<#y<<" :: "<<y<<"\t"<<#z<<" :: "<<z<<"\n";
//#define P pair<ll, ll>
#define dvec vector<vector<ll>>
//printf("%.10f\n")
//cout << fixed << setprecision(10);
template<class T> inline bool chmax(T& a, T b){if (a < b) { a = b; return true; } return false;}
template<class T> inline bool chmin(T& a, T b){if (a > b) { a = b; return true; } return false;}
ll INF = 1e+18;
int iINF = 1e9;


int main()
{
  string S, T; cin >> S >> T;
  int N = S.size();
  int M = T.size();
  sort(S.begin(), S.end());
  sort(T.begin(), T.end());

  int same = 0;
  for(auto x: S){
    for(auto y: T){
      if(x < y){
        cout << "Yes" << endl;
        return 0;
      }
      if(x == y){
        ++same;
        break;
      }
    }
  }

  if(same == N && N < M) cout << "Yes" << endl;
  else cout << "No" << endl;
}