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_array=gets.chomp.split(" ").map(&:to_i)
b_array=gets.chomp.split(" ").map(&:to_i)
c_array= []
(0..(N-1)).each do |i|
    c_array.push([a_array[i], b_array[i]])
end
c_sorted = c_array.sort_by {|e| e[1]}

a_sorted = a_array.sort

a_before = {}
a_after = {}

enable = false
a_sorted.each_with_index do |a, index|
    b = c_sorted[index][1]
    if a > b
        puts "No"
        exit
    end
    if !enable && a == c_sorted[index][0]
        enable = true
    end
    a_before[c_sorted[index][0]] = index
    a_after[a] = index
end

if enable || a_array.uniq.length == N
    puts "Yes"
    exit
end

c = 0
a = a_array[0]
start = a
loop do
    after_index = a_after[a]
    before_value = c_sorted[after_index][0]
    a = before_value
    c += 1
    break if a == start
end
if c >= N
    puts "No"
else
    puts "Yes"
end