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 pb push_back
#define all(v) (v).begin() , (v).end()
#define popcnt(x) __builtin_popcount(x)
#define inf 0x3f3f3f3f
#define watch(x) cout << (#x) << " is " << (x) << endl
#define rand() (rand() << 15 | rand())
using namespace std;
typedef long long  ll;
#define EPS 1e-9
#define PI acos(-1.0)

int main() {
   ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
   int n;
   cin >> n;
   vector<int> b(n);
   vector<pair<int ,int>> a(n);
   set<pair<pair<int , int> , int>> s;
   for(int i = 0 ; i < n ; ++i){
      cin >> b[i];
   }
   for(int i = 0 ; i < n ; ++i){
      cin >> a[i].first;
      a[i].second = i;
   }
   for(int i = 0 ; i < n ; ++i){
      s.insert({{b[i] , (a[i].first > b[i])} , i});
   }
   vector<pair<int , int>> sor(all(a));
   sort(all(sor));
   int cnt = 0;
   for(int i = n - 1 ; i >= 0 ; --i){
      int j = sor[i].second;
      if(b[j] > a[j].first){
         ++cnt;
         auto it = s.rbegin();
//         cout << it->first.first << ' ' <<  a[j].first << endl;
         if(it->first.first < a[j].first){
            cout << "No\n";
            return 0;
         }
         int k = it->second;
//         cout << j << ' ' << k << endl;
         swap(b[j] , b[k]);
         s.erase(*it);
      }
      else{
         s.erase({{b[j] , (a[i].first > b[i])} , j});
      }
   }
//   watch(cnt);
//   for(int i = 0 ; i < n ; ++i){
//      cout << b[i] << ' ' << a[i].first << endl;
//   }
   cout << (cnt <= n - 2 ? "Yes\n" : "No\n");
}