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;

class UnionFind{
    public:
    //親の番号を格納する。親だった場合は-(その集合のサイズ)
    vector<int> parent;

    UnionFind(int N){
        parent = vector<int>(N,-1);
    }

    //Aがどのグループに属しているか(Aの根)を調べる
    int root(int A){
        if(parent[A] < 0) return A;
        return parent[A]=root(parent[A]);
    }

    int size(int A){
        return -parent[root(A)];
    }

    bool unite(int A, int B) {
        A = root(A), B = root(B);
        if(A == B) return false; 

        if(size(A) < size(B)) swap(A,B);
        parent[A] += parent[B];
        parent[B] = A;
        return true;
    }

    bool same(int A, int B){
        return root(A)==root(B);
    } 
};

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);
    
    int n;
    cin>>n;
    UnionFind uni(n);
    array<int,2> a[n],b[n];
    for(int i=0;i<n;i++){
        int c;
        cin>>c;
        a[i] = {c,i};
    }
    for(int i=0;i<n;i++){
        int c;
        cin>>c;
        b[i] = {c,i};
    }
    sort(a,a+n);
    sort(b,b+n);
    for(int i=0;i<n;i++){
        if(a[i][0]>b[i][0]){
            cout << "No\n";
            return 0;
        }
        uni.unite(a[i][1],b[i][1]);
    }
    int cnt=0;
    for(int i=0;i<n;i++){
        if(i==uni.root(i))cnt++;
    }
    if(cnt>1){
        cout << "Yes\n";
    }
    else cout << "No\n";

}