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<cstdio>
#include<algorithm>
using namespace std;
inline int read(){
	register char ch=getchar();
	register int o=0;
	while(ch<'0'||ch>'9')ch=getchar();
	while(ch>='0'&&ch<='9'){
		o=(o<<3)+(o<<1)+(ch^48);
		ch=getchar();
	}
	return o;
}
int n,a[100001],b[100001];
int main(){
	n=read();
	for(register int i=1;i<=n;i++)a[i]=read();
	for(register int i=1;i<=n;i++)b[i]=read();
	sort(a+1,a+1+n);
	sort(b+1,b+1+n);
	for(register int i=1;i<=n;i++){
		if(a[i]>b[i]){
			puts("No");
			return 0;
		}
	}
	puts("Yes");
}