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++)
#define reps(i, n) for (int i = 1; i < (n)i++)
#define all(x) (x).begin(), (x).end()
#define rv(s) reverse((s).begin(), (s).end())
#define pii pair<int, int>
#define abs(a) llabs(a)
#define int long long
#define setout(n, x) setw(n) << setfill(x)
#define Fixed fixed << setprecision(10);
const long long mod = 1e9 + 7;

bool bl[1000010];
long long x[10000010], y[10000010], z[100000010];
signed main()
{

   cin.tie(0);
   ios::sync_with_stdio(false);

   int n, b, c, cnt = 0, ans = 0;
   string s, v;

   cin >> n;

   rep(i, n) cin >> x[i];
   rep(i, n) cin >> y[i];
   sort(x, x + n);
   sort(y, y + n);

   int a;
   if (n % 2 == 0)
      a = n / 2;
   else
      a = (n + 1) / 2;
   rep(i, a)
   {
      if (x[i] > y[i])
      {
         cout << "No" << '\n';
         return 0;
      }
      if (x[n - (i + 1)] > y[n - (i + 1)])
      {
         cout << "No" << '\n';
         return 0;
      }
   }
   cout << "Yes" << '\n';
}