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: Accepted)

#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;
    set<pair<int,int> > st;
    set<pair<int,int> > ::iterator it;
    for(int i=0; i<n; i++)
    {
        ll x;
        cin>>x;
        a.push_back(x);
    }
    for(int i=0; i<n; i++)
    {
        ll x;
        cin>>x;
        b.push_back(x);

    }
    for(int i=0;i<n;i++)
    {
        st.insert(make_pair(a[i],i));
    }
    int cnt=0;
    bool chk=0;
    for(int i=0;i<n;i++)
    {
        if(cnt==(n-2))
        {
            break;
        }
        pair<int,int> p=*(st.begin());
        if(p.first>b[i])
        {
            chk=1;
            break;
        }
        it=st.lower_bound(make_pair(b[i]+1,-1));
        it--;
        p=(*it);
        if(p.first != a[i])
        {
            cnt++;
            st.erase({a[i],i});
            a[p.second]=a[i];
            a[i]=p.first;
            st.erase(p);
            st.insert({a[p.second],p.second});
        }
        else
        {
            st.erase({a[i],i});
        }
    }
    if(chk==0)
    {
        for(int i=0;i<n;i++)
        {
            if(a[i]>b[i])
            {
                chk=1;
                break;
            }
        }
    }
    if(chk) cout<<"No"<<endl;
    else if(chk==0) cout<<"Yes"<<endl;


    return 0;
}