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.to_i

A = gets.split.map(&:to_i)
B = gets.split.map(&:to_i)

if A.zip(B).count { |a, b| a > b } > n - 2
  puts "No"
  exit
end

ag = A.group_by { |i| i }
bg = B.group_by { |i| i }

a_sum = 0
b_sum = 0

ag_key = ag.keys.sort.each

if ag.keys.max > bg.keys.max
  puts "No"
  exit
end

bg.keys.sort.each do |b|
  b_sum += bg[b].size

  begin
    while ag_key.peek <= b
      a_sum += ag[ag_key.next].size
    end
  rescue StopIteration
  end

  if a_sum < b_sum
    puts "No"
    exit
  end
end

puts "Yes"