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()))
xa = sorted([[a[i], i] for i in range(N)], key = lambda x: (x[0], x[1]))
xb = sorted([[b[i], i] for i in range(N)], key = lambda x: (x[0], x[1]))
for i in range(N):
  if xa[i][0] > xb[i][0]:
    print("No")
    exit(0)
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.root = [-1] * (n + 1)
    self.rnk = [0] * (n + 1)

  def Find_Root(self, x):
    if self.root[x] < 0:
      return x
    else:
      self.root[x] = self.Find_Root(self.root[x])
      return self.root[x]

  def Unite(self, x, y):
    x = self.Find_Root(x)
    y = self.Find_Root(y)
    if x == y:
      return 
    elif self.rnk[x] > self.rnk[y]:
      self.root[x] += self.root[y]
      self.root[y] = x
    else:
      self.root[y] += self.root[x]
      self.root[x] = y
      if self.rnk[x] == self.rnk[y]:
        self.rnk[y] += 1

  def isSameGroup(self, x, y):
    return self.Find_Root(x) == self.Find_Root(y)

  def Count(self, x):
    return -self.root[self.Find_Root(x)]
uf = UnionFind(N)
c = 0
#print(xa, xb)
for i in range(N):
  if xa[i][0] == xb[i][0]:
    xb[i][1] = xa[i][1]
for i in range(N):
  #print((xa[i][1], xb[i][1]))
  if uf.isSameGroup(xa[i][1], xb[i][1]):
    c += 1
  uf.Unite(xa[i][1], xb[i][1])
if c >= 2:
  print("Yes")
else:
  print("No")
#print(c)