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 (GCC 5.4.1) (judge verdict: Wrong Answer)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author yosiiii
 */


#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(long long int i=0;i<(n);++i)
typedef long long int ll;

class CSwaps {
public:
	void solve(std::istream& in, std::ostream& out) {
	    ll n;
	    in >> n;
	    vector<ll> a(n),b(n);
	    vector<pair<ll,ll>> ab(n);
	    rep(i,n){
	        in >> ab[i].first;
	    }
	    rep(i,n){
	        in >> ab[i].second;
	    }
	    sort(ab.begin(),ab.end());
	    rep(i,n){
	        a[i]=ab[i].first;
	        b[i]=ab[i].second;
	    }
	    sort(b.begin(),b.end());
	    ll c=0L;
	    rep(i,n){
	        if(a[i]>b[i]){
	            out << "No" << endl;
	            return;
	        }
	        if(b[i]!=ab[i].second)c++;
	    }
	    bool f=true;
	    for(int i=1;i<n;i++){
	        if(a[i-1]<=b[i]&&a[i]<=b[i-1]&&(b[i]==ab[i-1].second||b[i-1]==ab[i].second)){
	            f=false;
	            break;
	        }
	    }
	    if(c==n&&f){
	        out << "No" << endl;
	    }else{
	        out << "Yes" << endl;
	    }
	}
};


int main() {
	CSwaps solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}