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: Wrong Answer)

import numpy as np
n = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
A_mat = np.array(A)
B_mat = np.array(B)
C_mat = B_mat - A_mat
C = C_mat.tolist()
x = 10 ** 10
num = 0
for i in range(len(C)):
    if 0 <= C[i] < x:
        x = C[i]
        num = i
A_1 = A_mat.tolist()
B_1 = B_mat.tolist()
A_1.pop(num)
B_1.pop(num)

A_1.sort()
B_1.sort()

A1_mat = np.array(A_1)
B1_mat = np.array(B_1)

C1 = B1_mat - A1_mat
if np.all(C1 >= 0):
    print('Yes')
else:
    print('No')