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 <iostream>
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>
#include <map>
#include <iomanip>
#include <stdlib.h>
#include <queue>

using namespace std;

const int nmax = 1e9 + 7;
const long long INF = 1e18;
const double PI = 2 * asin(1);
typedef long long ll;


int main(){
  int N; cin >> N;
  vector <ll> A(N), B(N);

  for (int i = 0; i < N; i++) cin >> A[i];
  for (int i = 0; i < N; i++) cin >> B[i];

  bool flag = true;

  vector < pair<ll, int> > AP(N), BP(N);
  for (int i = 0; i < N; i++){
    AP[i] = make_pair(A[i], i);
    BP[i] = make_pair(B[i], i);
  }
  sort(AP.begin(), AP.end());
  sort(BP.begin(), BP.end());

  for (int i = 0; i < N; i++){
    if (AP[i].first > BP[i].first){
      flag = false;
    }
  }
    
  if (flag == true){
    int cnt = 0;
    for (int i = 0; i < N; i++){
      int now = 0;
      while (AP[i + now].first <= BP[i].first && i + now < N){
        now++;
      }
      if (i + now == N && now > 1){
        now--;
      }
      
      vector <int> A2(now), B2(now);
      for (int j = 0; j < now; j++){
        A2[j] = AP[i + j].second;
        B2[j] = BP[i + j].second;
      }
      sort(A2.begin(), A2.end());
      sort(B2.begin(), B2.end());

      int a = 0, b = 0;
      while (a < now && b < now){
        if (A2[a] == B2[b]){
          cnt++;
          a++; b++;
        }else{
          if (A2[a] < B2[b]) a++;
          else b++;
        }
      }
      i += now - 1;
    }

    if (cnt >= 1) cout << "Yes" << endl;
    else cout << "No" << endl;

  }else{
    cout << "No" << endl;
  }

  return 0;
}