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<math.h>
#include<algorithm>
#include<utility>
#include<queue>
#include<string.h>
#include<string>
#include<set>
#include<map>
#include<unordered_map>
#include<vector>
#include<functional>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
typedef pair<P,ll> Node;
const ll INF=2e18;
const ll MOD=1e9+7;

ll N;
ll a[100010];
ll b[100010];
multiset<ll> bSet;
ll aOptimizer[100010];
unordered_map< ll,set<ll> > optMap;
int main(){
    cin>>N;
    for(ll i=0;i<N;i++){
        cin>>a[i];
    }
    for(ll i=0;i<N;i++){
        cin>>b[i];
        bSet.insert(b[i]);
    }
    for(ll i=0;i<N;i++){
        auto it=bSet.lower_bound(a[i]);
        if(it==bSet.end()){
            cout<<"No"<<endl;
            return 0;
        }
        aOptimizer[i]=*it;
        bSet.erase(it);
    }
    for(ll i=0;i<N;i++){
        optMap[b[i]].insert(aOptimizer[i]);
    }

    for(ll i=0;i<N;i++){
        auto st_p=&(optMap[aOptimizer[i]]);
        if(st_p->find(b[i])!=st_p->end()){
            cout<<"Yes"<<endl;
            return 0;
        }
    }
    cout<<"No"<<endl;
   
    return 0;
}