#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define all(V) (V).begin(),(V).end()
#define MOD 998244353

int main(){
	int N;
	cin >> N;
	vector<pair<int, int>> A(N);
	for (int i = 0;i < N;i++) {
		cin >> A[i].second;
	}
	for (int i = 0;i < N;i++) {
		cin >> A[i].first;
	}
	sort(all(A));

	vector<int> B(N), C(N);
	for (int i = 0;i < N;i++) {
		B[i] = A[i].first;
		C[i] = A[i].second;
	}

	for (int i = 0;i < N;i++) {
		auto it = lower_bound(all(B), C[i]);
		if (it == B.end()) {
			cout << "No" << endl;
			return 0;
		}
		C[i] = *it;
	}

	vector<int> D = C;
	sort(all(D));
	bool db = 0;
	for (int i = 0;i < N;i++) {
		if (D[i] > B[i]) {
			cout << "No" << endl;
			return 0;
		}
		if (i != 0 && D[i] == D[i - 1])db = 1;
	}
	if (db) {
		cout << "Yes" << endl;
		return 0;
	}
	vector<int> E(N);
	for (int i = 0;i < N;i++) {
		auto it = lower_bound(all(D), C[i]);
		E[i] = it - D.begin();
	}

	int n = 0, next, cnt = 0;
	while (E[n] >= 0) {
		cnt++;
		next = E[n];
		E[n] = -1;
		n = next;
	}
	if (cnt == N)
		cout << "No" << endl;
	else
		cout << "Yes" << endl;
}
### Prompt

In cpp, your task is to solve 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 ll long long
#define all(V) (V).begin(),(V).end()
#define MOD 998244353

int main(){
	int N;
	cin >> N;
	vector<pair<int, int>> A(N);
	for (int i = 0;i < N;i++) {
		cin >> A[i].second;
	}
	for (int i = 0;i < N;i++) {
		cin >> A[i].first;
	}
	sort(all(A));

	vector<int> B(N), C(N);
	for (int i = 0;i < N;i++) {
		B[i] = A[i].first;
		C[i] = A[i].second;
	}

	for (int i = 0;i < N;i++) {
		auto it = lower_bound(all(B), C[i]);
		if (it == B.end()) {
			cout << "No" << endl;
			return 0;
		}
		C[i] = *it;
	}

	vector<int> D = C;
	sort(all(D));
	bool db = 0;
	for (int i = 0;i < N;i++) {
		if (D[i] > B[i]) {
			cout << "No" << endl;
			return 0;
		}
		if (i != 0 && D[i] == D[i - 1])db = 1;
	}
	if (db) {
		cout << "Yes" << endl;
		return 0;
	}
	vector<int> E(N);
	for (int i = 0;i < N;i++) {
		auto it = lower_bound(all(D), C[i]);
		E[i] = it - D.begin();
	}

	int n = 0, next, cnt = 0;
	while (E[n] >= 0) {
		cnt++;
		next = E[n];
		E[n] = -1;
		n = next;
	}
	if (cnt == N)
		cout << "No" << endl;
	else
		cout << "Yes" << endl;
}
```