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 = [int(a) for a in input().split()]
B = [int(b) for b in input().split()]

As = sorted(A)
Bs = sorted(B)


for i in range(N):
    if As[i]>Bs[i]:
        print("No")
        break
else:
    ALR = []
    l = 0
    r = 0
    for i in range(N):
        while r+1<=N-1 and As[r+1]<=Bs[i]:
            r += 1
        while l+1<=N-1 and As[l]>Bs[i]:
            l += 1
        ALR.append([As[i],Bs[l],Bs[r]])
    AB = [[a,b] for a,b in zip(A,B)]
    AB.sort(key = lambda x:x[0])
    cnt = 0
    for i in range(N):
        if AB[i][0] > AB[i][1]:
            cnt += 1
        elif ALR[i][2]<AB[i][1]:
            cnt += 1
    if cnt <= N-2:
        print("Yes")
    else:
        print("No")