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: Accepted)

#include "bits/stdc++.h"
#define ALL(x) x.begin(),x.end()
#define rep(i,n) for(int i=0;i<n;++i)

using namespace std;
typedef long long ll;

template<typename T>
T gcd(T a, T b){
   if (a%b == 0){
       return(b);
   }
   else{
       return(gcd(b, a%b));
   }
}

template<typename T>
T lcm(T a,T b){
    return a*b/gcd(a,b);
}

int main(void){
    vector<int>s;
    vector<int>t;
    string s_,t_;

    cin>>s_>>t_;
    rep(i,s_.length()){
        s.push_back(int(s_[i]));
    }
    rep(i,t_.length()){
        t.push_back(int(t_[i]));
    }
    sort(ALL(s));
    sort(ALL(t));
    reverse(ALL(t));
    rep(i,min(s.size(),t.size())){
        if(s[i]<t[i]){
            cout<<"Yes";
            return 0;
        }
        if(s[i]>t[i]){
            cout<<"No";
            return 0;
        }
    }
    if(s.size()<t.size()){
        cout<<"Yes";
    }
    else{
        cout<<"No";
    }
}
/*
*/