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: Accepted)

#include <iostream>
#include <limits.h>
#include <algorithm>
#include <bitset>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <list>
#include <map>
#include <numeric>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <cassert>

#define REP(i,n) for(int i=0;i<n;i++)
#define all(x) (x).begin(),(x).end()
#define mp make_pair
#define pb push_back
#define eb emplace_back

typedef long long ll;
using namespace std;

int main(void){
    cin.tie(0);
    ios::sync_with_stdio(false);
    // cout << fixed << setprecision(20);
    
    //入力を受け取る
    int n;cin >> n;
    vector<pair<int,int> > arr(n);
    for(int i = 0;i < n;i++){
        cin >> arr[i].second;
    }
    for(int i = 0;i < n;i++){
        cin >> arr[i].first;
    }
    //B側でソートする
    sort(arr.begin(),arr.end());
    //A_p1<=A_p2<=...<=A_pnとなるように順列Pを構成する
    vector<pair<int,int> > A(n);
    for(int i = 0;i < n;i++){
        A[i] = make_pair(arr[i].second,i);
    }
    sort(A.begin(),A.end());
    for(int i = 0;i < n;i++){
        if(A[i].first > arr[i].first){
            cout << "No" << '\n';
            return 0;
        }
    }
    vector<int> p(n);
    for(int i = 0;i < n;i++)p[i] = A[i].second;
    //順列pのサイクルを数える
    vector<int> used(n,0);
    int cycle = 0;
    for(int i = 0;i < n;i++){
        if(!used[i]){
            cycle++;
            int j = i;
            while(!used[j]){
                used[j] = 1;
                j = p[j];
            }
        }
    }
    if(cycle >= 2){
        cout << "Yes" << '\n';
        return 0;
    }
    //サイクルが1個だったとき、B_i>=P_i+1を満たすiがあるか？
    for(int i = 0;i < n-1;i++){
        if(arr[i].first >= arr[p[i+1]].second){
            cout << "Yes" << '\n';
            return 0;
        }
    }
    cout << "No" << '\n';
    return 0;
}