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 collections
import sys
input = sys.stdin.readline

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

table = collections.defaultdict(set)

for i in range(N):
    table[A[i]].add(B[i])

B.sort()
A_ = sorted(A)
count = 0
for i in range(N):
    if A_[i] <= B[i]:
        if B[i] in table[A[i]]:
            count += 1
    else:
        print("No")
        exit(0)

if count > 0:
    print("Yes")
else:
    tmp = []
    for i in range(N):
        if [A_[i], A[i]] in tmp:
            tmp.pop(tmp.index([A_[i], A[i]]))
            print("Yes")
            exit(0)
        else:
            tmp.append([A[i], A_[i]])

    print("No")