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 lower_bound(array, value)
    left = -1;
    right = array.length;
    while left + 1 < right
      mid = left + (right - left) / 2;
      if array[mid] > value  #>=
        right = mid
      else
        left = mid
      end
    end
    right
end

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


ab=a.zip(b).sort_by{|x,y| [y,x]}
asroted=a.sort

r = ab.each_with_index.map{|(x,y),i| [x,y,lower_bound(asroted,y)-i-1] }
#p r
if r.none?{|x,y,w| w<0 } and r.each_with_index.any?{|(x,y,w),i| ( i-w<0 || asroted[i-w] <= x) && x <= asroted[i]  }
    print 'Yes'
else
    print 'No'
end