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 Scala (2.13.1) (judge verdict: Accepted)

import java.util.Scanner

object Main extends App {
  val sc = new Scanner(System.in)
  val n = sc.nextInt()
  var a, b = new Array[Int](n)
  for (i <- Range(0, n)) {
    a(i) = sc.nextInt()
    b(i) = sc.nextInt()
  }
  a = a.sorted
  b = b.sorted
  if (n % 2 == 1) {
    println(b(n / 2) - a(n / 2) + 1)
  } else {
    println(b(n / 2) + b(n / 2 - 1) - a(n / 2) - a(n / 2 - 1) + 1)
  }
}