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)

c = []
n.times do |i|
  c[i] = [a[i], b[i]]
end
c.sort_by! { |u| u[0] }
c.sort_by! { |u| u[1] }

a.sort!

count = n - 2

n.times do |i|
  if c[i][0] <= c[i][1]
    a.delete_at(a.find_index(c[i][0]))
  else
    if count < 0
      puts 'No'
      exit
    end
    p = a.shift
    (i+1).upto(n-i) do |t|
      if c[t][0] == p
        c[i][0], c[t][0] = c[t][0], c[i][0]
        break
      end
    end
    if c[i][0] <= c[i][1]
      count -= 1
    else
      puts 'No'
      exit
    end
  end
end
puts 'Yes'