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.*;
import java.util.function.*;
import java.lang.*;
import java.io.*;


public class Main {
    static long medianx2(long[] A){
        long[] B = Arrays.copyOf(A,A.length);
        Arrays.sort(B);
        if(B.length %2 == 0) return B[B.length/2 - 1] + B[B.length/2];
        else return 2 * B[B.length / 2];
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        long[] A = new long[N];
        long[] B = new long[N];
        for(int n=0; n<N; n++){
            A[n] = sc.nextLong();
            B[n] = sc.nextLong();
        }
        long min = medianx2(A);
        long max = medianx2(B);
        System.out.println(N%2==0 ? 1+max-min : 1+(max-min)/2);
    }
}

