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.

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.

Examples

Input

2
1 2
2 3


Output

3


Input

3
100 100
10 10000
1 1000000000


Output

9991
import java.util.*;
public class Main {
        public static void main(String[] args){
                Scanner sc = new Scanner(System.in);
                int n = sc.nextInt();
                int[] a = new int[n];
                int[] b = new int[n];
                for(int i = 0 ; i < n ; i++){
                        a[i] = sc.nextInt();
                        b[i] = sc.nextInt();
                }
                sc.close();
                Arrays.sort(a);
                Arrays.sort(b);
                double owata = 0;
                double yokun = 0;
                if(n % 2 == 0){
                        owata = a[n / 2 - 1] + a[n / 2];
                        owata /= 2.0;
                        yokun = b[n / 2 - 1] + b[n / 2];
                        yokun /= 2.0;
                        yokun -= owata;
                        System.out.println((int)(yokun * 2) + 1);
                }else{
                        System.out.println(b[n / 2] - a[n / 2] + 1);
                }

        }
}//AC出たら泣いて喜ぶよ