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 <algorithm>

using namespace std;

#define out(v) cout<<v<<"\n"
#define rep(i,n) for(int i=0;i<(n);++i)

int main() {
  cin.tie(0); ios::sync_with_stdio(false);
  int N; cin >> N;

  pair<int, int> BA[N];
  int A[N], B[N];
  int sortA[N];
  rep(i, N) cin >> BA[i].second;
  rep(i, N) cin >> BA[i].first;

  sort(BA, BA+N);

  rep(i, N) sortA[i] = A[i] = BA[i].second;
  rep(i, N) B[i] = BA[i].first;

  sort(sortA, sortA+N);

  rep(i, N) {
    if (sortA[i] > B[i]) {
      cout << "???\n";
      return 0;
    }
  }
  // これで少なくともソートさえすればA<=Bを満たせると保証された

  int count = 0;
  for(int i=N-1;i>=0;--i) {
    if (A[i] <= B[i])
      ++count;
  }
  if (count <= 1) cout << "No\n";
  else cout << "Yes\n";

  return 0;
}