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;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)

int main()
{
ll n ;
cin >> n ;
vector<pair<ll,ll>> a;
rep(i, n){
  ll x ;
  cin >> x ;
  a.emplace_back(x,i);
}
vector<pair<ll,ll>> b;
rep(i, n){
  ll x ;
  cin >> x ;
  b.emplace_back(x,i);
}
sort(a.begin(),a.end());
sort(b.begin(),b.end());
rep(i,n){
  if(a[i].first>b[i].first){
    cout << "No" << endl;
    return 0;
  }
}

set<ll> s;
s.insert(b[0].second);
bool ok=0;
ll ind=0;
rep(i,n){
  if(i>ind){
    s.clear();
    ind=i;
  }
  while(ind!=n-1){
    if(b[ind].second>=a[ind+1].second){
      ind++;
      s.insert(b[ind+1].second);
    }
    else break;
  }
  if(s.find(a[i].second)!=s.end())ok=1;
}
if(ok){
  cout << "Yes" << endl;
}
else{
  cout << "No" << endl;
}
return 0;
}