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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;

class Program {

    static void Main (string[] args) {
        int N = int.Parse (Console.ReadLine ());
        long[] A = new long[N];
        long[] B = new long[N];
        for (int i = 0; i < N; i++) {
            string[] strtemp = Console.ReadLine ().Split (' ');
            A[i] = long.Parse (strtemp[0]);
            B[i] = long.Parse (strtemp[1]);
        }

        quickSortB2S (A);
        quickSortB2S (B);

        if (N % 2 == 0) {
            Console.WriteLine (B[N / 2] + B[N / 2 - 1] - A[N / 2] - A[N / 2 - 1] + 1);
        } else {
            Console.WriteLine (B[(N - 1) / 2] - A[(N - 1) / 2] + 1);
        }
    }

    static void quickSortB2S (long[] a) {
        quickSortB2S (a, 0, a.Length - 1);
    }

    static void quickSortB2S (long[] a, int left, int right) {
        if (left < right) {
            int i = left;
            int j = right;
            long tmp;
            long pivot = med3 (a[i], a[i + (j - i) / 2], a[j]);
            while (true) {
                while (a[i] > pivot) i++;
                while (pivot > a[j]) j--;
                if (i >= j) break;
                tmp = a[i];
                a[i] = a[j];
                a[j] = tmp;
                i++;
                j--;
            }
            quickSortB2S (a, left, i - 1);
            quickSortB2S (a, j + 1, right);
        }
    }

    static long med3 (long x, long y, long z) {
        if (x < y) {
            if (y < z) {
                return y;
            } else if (z < x) {
                return x;
            } else {
                return z;
            }
        } else {
            if (z < y) {
                return y;
            } else if (x < z) {
                return x;
            } else {
                return z;
            }
        }

    }

    //1000000007
}

//dotnet run --project test