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;

#define rep(i, n) for(int i = 0; i < (n); ++i)

typedef long long ll;
typedef pair<int, int> P;

const int MAX = 1e5 + 5;
const int INF = 1001001001;
const int MOD = 1e9 + 7;

int N;
vector<int> A, B;

int main(){
    cin >> N;

    A = vector<int>(N);
    B = vector<int>(N);

    rep(i, N) cin >> A[i];
    rep(i, N) cin >> B[i];

    vector<P> tmp(N);
    rep(i, N) tmp[i] = P(A[i], i);

    vector<P> Bs(N);
    rep(i, N) Bs[i] = P(B[i], i);
    sort(Bs.begin(), Bs.end());

    sort(tmp.begin(), tmp.end());
    sort(B.begin(), B.end());

    rep(i, N) {
        if (B[i] < tmp[i].first) {
            puts("No");
            return 0;
        }
    }

    vector<int> to(N);
    rep(i, N) {
        to[ tmp[i].second ] = i;
    }

    vector<bool> vis(N, false);
    int cnt = 0;
    rep(i, N) {
        int x = i;
        bool flg = false;
        while (!vis[x]) {
            vis[x] = true;
            x = to[x];
            flg = true;
        }

        if (flg) cnt++;
    }

    if (2 <= cnt) {
        puts("Yes");
        return 0;
    }

    bool ans = false;
    rep(i, N - 1) {
        if (tmp[i + 1].first <= B[i]) ans = true;
    }

    if (ans) {
        puts("Yes");
    } else {
        puts("No");
    }
}