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<bits/stdc++.h>
#define ii pair<int,int>
#define mp make_pair
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define INF 100000000000000000
#define int long long int
#define modulo 1000000007
using namespace std;

int32_t main(){
      ios_base::sync_with_stdio(false);
      cin.tie(NULL);
      int n;
      cin>>n;
      vector<int> A(n),B(n),a,b;
      for(int i=0;i<n;i++)cin>>A[i];
      for(int i=0;i<n;i++)cin>>B[i];
      a=A,b=B;
      sort(all(a),greater<int>()),sort(all(b),greater<int>());
      for(int i=0;i<n;i++){
            if(a[i]>b[i]){
                  cout<<"No";
                  return 0;
            }
      }
      int cnt=0;
      vector<ii> arr;
      for(int i=0;i<n;i++){
            arr.pb({B[i],A[i]});
      }
      sort(all(arr),greater<ii>());
      for(int i=0;i<n;i++){
            if(arr[i].first>=arr[i].second)cnt++;
      }
      for(int i=1;i<n;i++){
            if(arr[i].first==arr[i-1].first){
                  cnt++;
            }
      }
      if(cnt>0)
      cout<<"Yes";
      else cout<<"No";
}