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)

#include <bits/stdc++.h>
#define MAX (ll)(2e5+5)
#define MOD (ll)(998244353)
#define INF (ll)(1e18 + 3)
#define PI (double)(3.14159265)

using namespace std;
using ll = long long;

int main () {
	int n;
	cin >> n;
	pair<int, int> aa[n], ar[n], br[n];
	int ga[n], gb[n];
	for (int i = 0; i < n; i++) {
		cin >> ar[i].first;
		ar[i].second = i;
		aa[i].first = ar[i].first;
	}	
	for (int i = 0; i < n; i++) {
		cin >> br[i].first;
		br[i].second = i;
		aa[i].second = br[i].first;
	}	
	sort (ar, ar + n);
	sort (br, br + n);
	for (int i = 0; i < n; i++) {
		if (ar[i].first > br[i].first) {
			cout << "No\n";
			return 0;
		}
	}
	int cc = 1;
	for (int i = n - 1; i >= 0;) {
		int vv = ar[i].first;
		while (i >= 0 && br[i].first >= vv) {	
			ga[ar[i].second] = cc;
			gb[br[i].second] = cc;
			i--;
		}
		cc++;
	}
	bool fl = 0;
	set<pair<int, int>> sp;
	for (int i = 0; i < n; i++) {
		if (ga[i] == gb[i]) {
			fl = 1;
			break;
		}
		if (sp.count (make_pair (gb[i], ga[i]))) {
			fl = 1;
			break;
		}
		sp.insert (make_pair (ga[i], gb[i]));
	}
	if (fl) {
		cout << "Yes\n";
	}
	else {
		cout << "No\n";
	}
}