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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))

A_sort = sorted(A)
B_sort = sorted(B)

for i in range(len(A)):
    if A_sort[i] > B_sort[i]:
        print("No")
        exit()

tmp = 0
swap_cnt = 0
for i in range(len(A)):
    for j in range(i, len(A)):
        if A[i] > A[j]:
            tmp = A[i]
            A[i] = A[j]
            A[j] = tmp
            swap_cnt += 1
      
print("Yes" if swap_cnt <= N-2 else "No")