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)

def ja;  puts'Yes'; exit end
def nein; puts'No'; exit end

N = gets.to_i
A, B = $<.map{|ln| ln.split.map(&:to_i) }

IA = (0...N).sort_by{|i| A[i] }
IB = (0...N).sort_by{|i| B[i] }
A’ = IA.map{|i| A[i] }
B’ = IB.map{|i| B[i] }

nein unless (0...N).all?{|i| A’[i]<=B’[i]  }

ja if (0..N-2).any?{|i|
	(i+1..N-1).take_while{|j| A’[j]<=B’[i] }.any?{|j|
		IA[i]==IB[j] || IA[j]==IB[i]
	}
}

visited, i = [nil]*N, 0
until visited[IA[i]]
	visited[IA[i]] = 1
	i = IB[IA[i]]
end
ja if visited.any?(&:nil?)

nein