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: Runtime Error)

def check(a2, b2)
    for i in 0...n
        if a2[i] > b2[i]
            return -1
        end
        if a2[i] == b2[i]
            return 1
        end
    end
    return 0
end

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

aa = a.sort
bb = b.sort
for i in 0...n
    if aa[i] > bb[i]
        puts "No"
        return
    end
end

for i in 0...n
    if a[i] == b[i]
        puts "Yes"
        return
    end
end

for i in 0...n
    for j in i+1...n
        if a[i] == b[j] && a[j] == b[i]
            puts "Yes"
            return
        end
    end
end

puts "No"