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 (2.7.1) (judge verdict: Wrong Answer)

def yes!; puts'Yes'; exit end
def no!; puts'No'; exit end

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

I = (0...N).sort_by{|i| B[i] }

LB = A.map{|a|
	I.bsearch_index{|i| a<=B[i] }||N
}
LB.sort.then{|lbs|
	no! unless lbs.each_with_index.all?{|lb,i| lb<=i }
	yes! if lbs.each_cons(2).any?(&:uniq!)
}

i,v,V = 0,0,[nil]*N
until V[i]
	V[i] = v+=1
	i = LB[i]
end
v<N ? yes! : no!