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)

#pragma warning(disable:4996)
#include<stdio.h>
#include<stdlib.h>
#include<iostream>
#include<algorithm>
#include<string.h>
#include<math.h>
#include<time.h>
#include<iomanip>
using namespace std;
typedef unsigned long long ull;

int asc(const void* a, const void* b) {
	return *(int*)a - *(int*)b;
}

int main() {
	int n, a[10000], b[100000];
	int a_max = 0, b_max = 0;
	int count = 0;
	cin >> n;
	for (int i = 0; i < n; ++i) {
		cin >> a[i];
		if (a_max < a[i]) {
			a_max = a[i];
		}
	}
	for (int i = 0; i < n; ++i) {
		cin >> b[i];
		if (b_max < b[i]) {
			b_max = b[i];
		}
		if (a[i] > b[i]) {
			++count;
			if (count < n - 2) {
				cout << "No" << endl;
			}
		}
	}
	if (a_max > b_max) {
		cout << "No" << endl; 
		return 0;
	}

	qsort(a, n, sizeof(a[0]), asc);
	qsort(b, n, sizeof(b[0]), asc);

	for (int i = 0; i < n; ++i) {
		if (a[i] > b[i]) {
			cout << "No" << endl;
			return 0;
		}
	}

	cout << "Yes" << endl;
	return 0;
}

/*
1 2 3 3 4 6
2 2 3 3 4 8
*/