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)

require 'pp'
$DEBUG ? define_method(:dpp){|e|pp e} : define_method(:dpp){|e|}

# 入力値を数値で返却する
def gets_i()
  gets.chomp.to_i
end

# 空白区切の入力値を数値の配列で返却する
def gets_i_list()
  gets.chomp.split(" ").map(&:to_i)
end

N = gets_i
a_list, b_list = [], []
N.times do |i|
  a_list[i], b_list[i] = gets_i_list
end

dpp a_list
dpp b_list

if N.even?
  i1, i2 = N/2 - 1, N/2
  a1, b1 = a_list[i1], b_list[i1]
  a2, b2 = a_list[i2], b_list[i2]
  puts (b1 + b2) - (a1 + a2) + 1
else
  i1 = N/2
  a1, b1 = a_list[i1], b_list[i1]
  puts b1 - a1 + 1
end