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: Wrong Answer)

class Median
  def initialize(a1, a2)
    @little = [a1, a2].min
    @much = [a1, a2].max
    @less = 0
    @more = 0
  end
  
  def add(a)
    if a < @little
      if @less <= @more
        @less += 1
      else
        @more += 1
        @much = @little
        @little = a
      end
    elsif a < @much
      if @less <= @more
        @less += 1
        @little = a
      else
        @more += 1
        @much = a
      end
    else
      if @less <= @more
        @less += 1
        @little = @much
        @much = a
      else
        @more += 1
      end
    end
  end
  
  def calc
    if @less == @more
      @little + @much
    elsif @less < @more
      @much
    else
      @little
    end
  end
end

n = gets.to_i

a1, b1 = gets.split.map &:to_i
a2, b2 = gets.split.map &:to_i

m_a = Median.new(a1, a2)
m_b = Median.new(b1, b2)

(2...n).each do
  a, b = gets.split.map &:to_i
  
  m_a.add a
  m_b.add b
end

puts m_b.calc - m_a.calc + 1