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<cstring>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<string>
#include<map>
#include<set>
#include<vector>
using namespace std;
typedef long long ll;
ll a[100005];
ll b[100005];
ll c[100005];
ll d[100005];
typedef pair<ll,ll>q;
set<q>mp;
int main()
{
    ll n,flag=1,flag1=0;
    cin>>n;
    for(ll i=0; i<n; i++)
    {
        scanf("%lld",&a[i]);
        c[i]=a[i];
    }
    for(ll i=0; i<n; i++)
    {
        scanf("%lld",&b[i]);
        d[i]=b[i];
    }
    sort(a,a+n);
    sort(b,b+n);
    for(ll i=0; i<n; i++)
    {
        mp.insert(make_pair(a[i],b[i]));
        if(a[i]>b[i])
        {
            flag=0;
            break;
        }
    }
    if(flag)
    {
        for(ll i=0; i<n; i++)
        {
            if(c[i]<=d[i])
                flag1=1;
        }
    }
    if(flag&&flag1)
        printf("Yes");
    else
        printf("No");


}
/*
5
5
1 5 4 2 3
1 2 5 4 3
*/