#include<bits/stdc++.h>

using namespace std;

#define fi first
#define se second
#define mp make_pair
#define pb push_back

const int N=110000;
typedef long long LL;
const LL mod=1e9+7;

int n;
int a[N],b[N];
struct node
{
	int id,w;
	friend bool operator < (node a,node b)
	{
		if (a.w!=b.w) return a.w<b.w;
		return a.id<b.id;
	}
}c[N],d[N];
int sum[N],psum[N],nsum[N];
int ys[N],pp[N];
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		c[i].w=a[i];
		c[i].id=i;
	}
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&b[i]);
		d[i].w=b[i];
		d[i].id=i;
	}
	sort(c+1,c+1+n);
	sort(d+1,d+1+n);
	int flag=0;
	for (int i=1;i<=n;i++)
		ys[d[i].id]=i;
	for (int i=1;i<=n;i++)
		if (c[i].w>d[i].w)
		{
			flag=1;
			break;
		}
	if (flag)
	{
		printf("No\n");
		return 0;
	}
	flag=0;
	for (int i=2;i<=n;i++)
		if (c[i].w<=d[i-1].w)
		{
			flag=1;
			break;
		}
	if (flag)
	{
		printf("Yes\n");
		return 0;
	}
	int num=0,cur=1;
	while (!pp[cur])
	{
		num++,pp[cur]=1;
		cur=ys[c[cur].id];
	}
	if (num==n) printf("No\n");
	else printf("Yes\n");
	return 0;
}
### Prompt

Please formulate a CPP solution to the following problem:

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`.

Examples

Input

3
1 3 2
1 2 3


Output

Yes


Input

3
1 2 3
2 2 2


Output

No


Input

6
3 1 2 6 3 4
2 2 8 3 4 3


Output

Yes

### Response

```cpp
#include<bits/stdc++.h>

using namespace std;

#define fi first
#define se second
#define mp make_pair
#define pb push_back

const int N=110000;
typedef long long LL;
const LL mod=1e9+7;

int n;
int a[N],b[N];
struct node
{
	int id,w;
	friend bool operator < (node a,node b)
	{
		if (a.w!=b.w) return a.w<b.w;
		return a.id<b.id;
	}
}c[N],d[N];
int sum[N],psum[N],nsum[N];
int ys[N],pp[N];
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		c[i].w=a[i];
		c[i].id=i;
	}
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&b[i]);
		d[i].w=b[i];
		d[i].id=i;
	}
	sort(c+1,c+1+n);
	sort(d+1,d+1+n);
	int flag=0;
	for (int i=1;i<=n;i++)
		ys[d[i].id]=i;
	for (int i=1;i<=n;i++)
		if (c[i].w>d[i].w)
		{
			flag=1;
			break;
		}
	if (flag)
	{
		printf("No\n");
		return 0;
	}
	flag=0;
	for (int i=2;i<=n;i++)
		if (c[i].w<=d[i-1].w)
		{
			flag=1;
			break;
		}
	if (flag)
	{
		printf("Yes\n");
		return 0;
	}
	int num=0,cur=1;
	while (!pp[cur])
	{
		num++,pp[cur]=1;
		cur=ys[c[cur].id];
	}
	if (num==n) printf("No\n");
	else printf("Yes\n");
	return 0;
}
```