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>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
ll a[100005],b[100005];
int main(){
  ll n;
  cin>>n;
  for(int i=0;i<n;i++) cin>>a[i];
  for(int i=0;i<n;i++) cin>>b[i];
  vector<P> pv,av;
  for(int i=0;i<n;i++) av.push_back(P(a[i],i+1));
  sort(av.begin(),av.end());
  sort(b,b+n);
  for(int i=0;i<n;i++){
    pv.push_back(P(b[i],av[i].second));
  }
  sort(pv.begin(),pv.end());
  for(int i=0;i<n;i++){
    if(av[i].first>pv[i].first){
      cout<<"No"<<endl;
      return 0;
    }
  }
  vector<bool> used(100005,false);
  ll pos=1;
  while(!used[pos]){
    used[pos]=true;
    pos=pv[pos-1].second;
  }
  bool f=true;
  for(int i=1;i<=n;i++){
    if(!used[i]) f=false;
  }
  if(!f){
    cout<<"Yes"<<endl;
    return 0;
  }
  for(int i=0;i<n-1;i++){
    if(av[i+1].first<=pv[i+1].first){
      cout<<"Yes"<<endl;
      return 0;
    }
  }
  cout<<"No"<<endl;
  return 0;
}