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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n = gets.chomp.to_i
a = gets.chomp.split.map(&:to_i)
b = gets.chomp.split.map(&:to_i)

aa = a.sort
bb = b.sort

n.times do |i|
  if aa[i] > bb[i]
    puts 'No'
    exit
  end
end

one_index = a.index(1)
1.upto(n) do |i|
  index = aa.index(i)
  if index == one_index && i != n
    puts 'Yes'
    exit
  end
end

(n-1).times do |i|
  if aa[i+1] <= bb[i]
    puts 'Yes'
    exit
  end
end
puts 'No'