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>
#define rep(i, n) for(int i=0; i<(n); ++i)
#define chmin(x,y) x = min(x,y)
#define chmax(x,y) x = max(x,y)
using namespace std;
using Graph = vector<vector<int>>;
typedef long long ll;
const int inf = INT_MAX;
const ll INF = 1LL << 60;
const ll mod = 1e9+7;

int main() {
    int n;
    cin >> n;
    vector<ll> A(n), B(n), sA(n), sB(n);
    rep(i,n){
        cin >> A[i];
        sA[i] = A[i];
    }
    rep(i,n){
        cin >> B[i];
        sB[i] = B[i];
    }

    sort(sA.begin(), sA.end());
    sort(sB.begin(), sB.end());
    int count = 0;
    int cc = 0;
    rep(i, n){
        if(A[i]<=B[i]) count++;
        if(sA[i]<=sB[i]){
            cc++;
        }else{
            cout << "No" << endl;
            return 0;
        }
    }

    if(cc <= n-2){
        cout << "Yes" << endl;
    }else{
        cout << "No" << endl;
    }

    return 0;
}