Problem:
Score : 600 points

Problem Statement

Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N.
Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:

Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.

Constraints

2 \leq N \leq 10^5

1 \leq A_i,B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

3
1 3 2
1 2 3

Sample Output 1

Yes

We should swap the values of A_2 and A_3.

Sample Input 2

3
1 2 3
2 2 2

Sample Output 2

No

Sample Input 3

6
3 1 2 6 3 4
2 2 8 3 4 3

Sample Output 3

Yes

Solution in C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<iostream>
#include<string>
#include<vector>
#include<numeric>
#include<algorithm>
#include<cmath>
#include<map>

using namespace std;

int main(){

    int N, i;
    cin >> N;

    vector<unsigned long> A(N), B(N);
    for(i=0; i<N; i++) cin >> A.at(i);
    for(i=0; i<N; i++) cin >> B.at(i);

    unsigned long count = 0;
    for(i=N-1; i>=0; i--){
        if(A.at(i) > B.at(i)){
            count++;
        }
    }

    if(count >= N-1){
        cout << "No" << endl;
        return 0;
    }
    
    sort(A.begin(), A.end());
    sort(B.begin(), B.end());

    for(i=N-1; i>=0; i--){
        if(A.at(i) > B.at(i)){
            cout << "No" << endl;
            return 0;
        }
    }

    cout << "Yes" << endl;

    return 0;
}