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;


int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    int n;
    cin>>n;
    vector<ll> a,b,c,d;
    for(int i=0; i<n; i++)
    {
        ll x;
        cin>>x;
        a.push_back(x);
        c.push_back(x);
    }
    map<ll,ll> mp,mpp,mop;

    for(int i=0; i<n; i++)
    {
        ll x;
        cin>>x;
        mp[x]=max(mp[x],a[i]);
        mpp[x]++;
        if(mpp[x]==1)
        {
            mop[x]=a[i];
        }
        else
        {
            mop[x]=min(mop[x],a[i]);
        }
        b.push_back(x);
        d.push_back(x);
    }
    sort(a.begin(),a.end());
    sort(b.begin(),b.end());
    bool chk=0;
    for(int i=0; i<n; i++)
    {
        if(a[i]<=b[i])
        {

        }
        else chk=1;
    }
    if(chk)
    {
        cout<<"No"<<endl;
    }
    else
    {
        for(int i=0; i<n; i++)
        {
            int dorkar=i;
            int nw=upper_bound(a.begin(),a.end(),b[i])-a.begin();
            dorkar++;
            ll req=mp[b[i]];
            if(req<=b[i])
            {
                nw--;
            }
            req=mop[b[i]];
            if(req<=b[i])
            {
                nw--;
            }
            if(nw>dorkar)
            {
                chk=1;
            }

        }
        if(chk) cout<<"Yes"<<endl;
        else cout<<"No"<<endl;
    }

    return 0;
}