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: Accepted)

def main():
    import sys
    read = sys.stdin.buffer.read
    readline = sys.stdin.buffer.readline
    readlines = sys.stdin.buffer.readlines

    import numpy as np

    N = int(readline())
    A = np.array(readline().split(), np.int32)
    B = np.array(readline().split(), np.int32)

    idx = B.argsort(); B = B[idx]; A = A[idx]

    Asorted = np.msort(A)
    if any(Asorted > B):
        print('No')
        return

    if any(Asorted[1:] <= B[:-1]):
        print('Yes')
        return

    perm = A.argsort().tolist()
    x = 0
    period = 0
    while True:
        period += 1
        x = perm[x]
        if x == 0:
            break

    print('Yes' if period != N else 'No')
    return

main()