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)

import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def resolve():
    n=int(input())
    A=list(map(int,input().split()))
    B=list(map(int,input().split()))
    C=sorted(A)
    D=sorted(B)

    # C[i]<=D[i] でなければ不可能
    if(any(C[i]>D[i] for i in range(n))):
        print("No")
        return

    # 1つでもC[i+1]<=D[i]があれば可能
    if(any(C[i+1]<=D[i] for i in range(n-1))):
        print("Yes")
        return

    # このどちらでもないとき、A のソートがn-1のサイクルになると不可能
    # B をソートさせて、それに対応するように A のソートを行う
    F=[(b,i) for i,b in enumerate(B)]
    F.sort()
    E=[0]*n
    for i in range(n):
        j=F[i][1]
        E[j]=(A[i],i)

    # 0から始めて、0に返ってくる最小回数を数える
    cnt=1
    j=E[0][1]
    while(j!=0):
        cnt+=1
        j=E[j][1]

    if(cnt<n-1):
        print("Yes")
    else:
        print("No")

resolve()