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 C# (Mono-mcs 6.8.0.105) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		int[][]A = new int[N][];
		for(var i=0;i<N;i++){
			A[i] = new int[2];
		}
		for(var i=0;i<N;i++){
			string[] str = Console.ReadLine().Split();
			A[i][0] = int.Parse(str[0]);
			A[i][1] = int.Parse(str[1]);
		}
		Array.Sort(A,(x,y)=>x[0]-y[0]);
		int ans = 0;
		if(N%2==1){
			int a1 = A[N/2][0];
			Array.Sort(A,(x,y)=>x[1]-y[1]);
			int a2 = A[N/2][1];
			ans = a2-a1+1;
		} else {
			int a1 = A[N/2-1][0];
			int a2 = A[N/2][0];
			Array.Sort(A,(x,y)=>x[1]-y[1]);
			int b1 = A[N/2-1][1];
			int b2 = A[N/2][1];
			ans = a2+b2-(a1+b1)+1;
		}
		Console.WriteLine(ans);
	}
}