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;

/* メモリ食い過ぎ注意 */
#define int long long

typedef long long ll;

int euclid(int a, int b)
{
    if (a < b)
        euclid(b, a);
    if (b == 0)
        return a;
    int r;
    while ((r = a % b))
    {
        a = b;
        b = r;
    }
    return b;
}

/* define const */
const ll INF = (1ll << 60);
const ll MOD = (ll)1e9 + 7;
/* end defineing */

signed main()
{
    string s;
    string t;
    cin >> s >> t;

    vector<char> vs;
    vector<char> vt;

    for (int i = 0; i < s.size(); i++)
        vs.push_back(s[i]);
    for (int i = 0; i < t.size(); i++)
        vt.push_back(t[i]);

    sort(vs.begin(), vs.end(), greater<char>());
    sort(vt.begin(), vt.end(), greater<char>());

    string ss = "";
    string tt = "";

    for (int i = 0; i < vs.size(); i++)
        ss += vs[i];
    for (int i = 0; i < vt.size(); i++)
        tt += vt[i];

    if (ss < tt)
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
}