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 = Array.new(N)
a2 = Array.new(N)
b = Array.new(N)
b2 = Array.new(N)
str = gets.split
for i in 0...N do
    a[i] = str[i].to_i
end
str = gets.split
for i in 0...N do
    b[i] = str[i].to_i
end
a2 = a.sort
b2 = b.sort
for i in 0...N do
    if a2[i] > b2[i]
        puts "No"
        exit
    end
end
for i in 1...N do
    if a2[i] <= b2[i-1]
        puts "Yes"
        exit
    end
end
c = Array.new(N){Array.new(2)}
for i in 0...N do
   c[i][0] = a[i]
   c[i][1] = b[i]
end
c.sort_by! {|x| x[0]}
f = 1
g = 0
j = 0
for i in 0...N-1 do
    if f == 1
        if c[i][1] > b2[i+1]
            f = 0
            g = 0
            j = i + 2
            while c[i][1] > b2[j]
                j += 1
            end
        elsif c[i][1] == b2[i+1]
            f = 0
            g = 1
            j = 1
        else
            puts "Yes"
            exit
        end
    else
        if g == 0
            if c[i][1] != b2[i-1]
                puts "Yes"
                exit
            end
            if i == j
                f = 1
            end
        else
            if c[i][1] == b2[i+1]
                j += 1
            elsif c[i][1] == b2[i-j] && j > 1
                f = 1
            else
                puts "Yes"
                exit
            end
        end
    end
end
puts "Yes"