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
input = sys.stdin.readline
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
bi = [[b[i],i] for i in range(n)]
bi.sort()
flg = 0
if len(set(b)) == n:
  for i in range(n):
    bi[i][0] = i
  bi.sort(key = lambda x:x[1])
  idc = list(zip(*bi))[0]
  cnt = 0
  plc = 0
  while True:
    plc = idc[plc]
    cnt += 1
    if plc == 0:
      break
  if cnt == n:
    flg = 1
a.sort()
b.sort()
for x,y in zip(a,b):
  if x > y:
    print("No")
    exit()
if not flg:
  print("Yes")
else:
  for i in range(1,n):
    if a[i] <= b[i-1]:
      print("Yes")
      exit()
  print("No")