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: Accepted)

using static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var n = long.Parse(ReadLine());
			var listA = new long[n];
			var listB = new long[n];

			for(var i = 0; i < n; i++)
			{
				var line = ReadLine().Split(' ').Select(value => long.Parse(value)).ToArray();
				listA[i] = line[0];
				listB[i] = line[1];
			}

			listA = listA.OrderBy(value => value).ToArray();
			listB = listB.OrderBy(value => value).ToArray();

			if(n % 2 == 1)
			{
				WriteLine(Abs(listA[(n + 1) / 2 - 1] - listB[(n + 1) / 2 - 1]) + 1);
			}
			else
			{
				double medianA = (listA[n / 2 - 1] + listA[n / 2]) / 2.0;
				double medianB = (listB[n / 2 - 1] + listB[n / 2]) / 2.0;
				WriteLine((long)(Abs(medianA - medianB) * 2) + 1);
			}
		}
	}
}