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 <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#define _USE_MATH_DEFINES
#include <cmath>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iostream>
#include <iomanip>
#include <iterator>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()

const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007; // 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};

struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(10);
  }
} iosetup;
/*-------------------------------------------------*/
int main() {
  int n; cin >> n;
  vector<int> a(n), b(n);
  vector<pair<int, int> > sorted_a(n);
  REP(i, n) {
    cin >> a[i];
    sorted_a[i] = {a[i], i};
  }
  REP(i, n) cin >> b[i];
  vector<int> sorted_b(b);
  sort(ALL(sorted_a));
  sort(ALL(sorted_b));
  REP(i, n) {
    if (sorted_a[i].first > sorted_b[i]) {
      cout << "No\n";
      return 0;
    }
  }
  vector<int> pos(n);
  REP(i, n) pos[sorted_a[i].second] = i;
  vector<bool> visited(n, false);
  int now = 0;
  visited[now] = true;
  while (true) {
    now = pos[now];
    if (visited[now]) break;
    visited[now] = true;
  }
  REP(i, n) {
    if (!visited[i]) {
      cout << "Yes\n";
      return 0;
    }
  }
  FOR(i, 1, n) {
    if (sorted_a[i].first <= b[i - 1]) {
      cout << "Yes\n";
      return 0;
    }
  }
  cout << "No\n";
  return 0;
}