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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))

aa = sorted(a)
bb = sorted(b)

for i in range(n):
    if aa[i] > bb[i]:
        print('No')
        exit()

ab = []

for i in range(n):
    ab.append([a[i],b[i]])

ab = sorted(ab, key=lambda x:(x[1],x[0]))


if len(set(aa)) < n:
    print('Yes')
    exit()

for i in range(n):
    if aa[i] == ab[i][0]:
        print('Yes')
        exit()

from collections import defaultdict
d = defaultdict(int)

for i in range(n):
    d[aa[i]] += i

abd = [0]*n

for i in range(n):
    abd[i] = d[ab[i][0]]

for i in range(n):
    if abd[abd[i]] == i:
        print('Yes')
        exit()

print('No')