Problem:
Score : 500 points

Problem Statement

There are N integers X_1, X_2, \cdots, X_N, and we know that A_i \leq X_i \leq B_i.
Find the number of different values that the median of X_1, X_2, \cdots, X_N can take.

Notes

The median of X_1, X_2, \cdots, X_N is defined as follows. Let x_1, x_2, \cdots, x_N be the result of sorting X_1, X_2, \cdots, X_N in ascending order.

If N is odd, the median is x_{(N+1)/2};

if N is even, the median is (x_{N/2} + x_{N/2+1}) / 2.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq B_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
:
A_N B_N

Output

Print the answer.

Sample Input 1

2
1 2
2 3

Sample Output 1

3

If X_1 = 1 and X_2 = 2, the median is \frac{3}{2};

if X_1 = 1 and X_2 = 3, the median is 2;

if X_1 = 2 and X_2 = 2, the median is 2;

if X_1 = 2 and X_2 = 3, the median is \frac{5}{2}.

Thus, the median can take three values: \frac{3}{2}, 2, and \frac{5}{2}.

Sample Input 2

3
100 100
10 10000
1 1000000000

Sample Output 2

9991

Solution in Ruby (2.7.1) (judge verdict: Accepted)

class E169
  def call(n, x_s)
    a_s = x_s.map {|x| x[0]}.sort
    b_s = x_s.map {|x| x[1]}.sort
    a_center = center(n, a_s)
    b_center = center(n, b_s)
    b_center - a_center + 1
  end

  def center(n, nums)
    if n.even?
      (nums[(n / 2 - 1)] + nums[(n / 2)])
    else
      nums[(n / 2)]
    end
  end

  def main
    n = gets.to_i
    ab_s = readlines.map { |x| x.split(' ').map { |y| y.to_i } }
    puts call(n, ab_s)
  end
end

E169.new.main