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)

#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<sstream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<climits>
#include<cmath>
#include<string>
#include<vector>
#include<set>
#include<map>
#include<queue>
#include<numeric>
#include<functional>
#include<algorithm>
#include<bitset>
#include<tuple>
#include<unordered_set>
#include<unordered_map>
#include<random>
#include<array>
#include<cassert>
using namespace std;
#define INF (1<<29)
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define all(v) v.begin(),v.end()
#define uniq(v) v.erase(unique(all(v)),v.end())


int n;
int a[100000];
int b[100000];

bool solve() {
	cin >> n;
	rep(i, n)cin >> a[i];
	rep(i, n)cin >> b[i];

	vector<int> va(a, a + n), vb(b, b + n);

	sort(a,a+n);
	sort(b,b+n);

	rep(i,n) {
		if (a[i] > b[i]) {
			return false;
		}
	}

	rep(i,n) {
		int cnt = upper_bound(a, a + n, b[i]) - a;
		if (cnt != i+1) {
			return true;
		}
	}
	
	unordered_map<int, int> idxs;
	vector<int> pos(n);
	rep(i, n)idxs[va[i]] = i;
	rep(i, n) {
		int idx = upper_bound(a, a + n, vb[i]) - a - 1;
		pos[i] = idxs[a[idx]];
	}

	rep(i, n) {
		if (i == pos[i] || i == pos[pos[i]]) {
			return true;
		}
	}


	return false;
}


int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	cout << (solve() ? "Yes" : "No") << endl;



	return 0;
}