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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.Scanner;

public class Main {
	static long searchLow(long A[] , long B[]){
		long left = 0;
		long right = 1000000000;
		int N = A.length;
		while(right - left > 1){
			long mid = (left + right) / 2;
			int large = 0;			
			int small = 0;
			for(int i = 0 ; i < A.length ; ++i){
				if(mid < A[i]){
					++large;
				}
				if(mid > B[i]){
					++small;
				}
			}
			int other = A.length - small - large;
			if(small + other > N / 2){
				right = mid;
			}else{
				left = mid;
			}
		}
		return right;
	}
	static long searchHigh(long A[] , long B[]){
		long left = 0;
		long right = 1000000000;
		int N = A.length;
		while(right - left > 1){
			long mid = (left + right) / 2;
			int large = 0;			
			int small = 0;
			for(int i = 0 ; i < A.length ; ++i){
				if(mid < A[i]){
					++large;
				}
				if(mid > B[i]){
					++small;
				}
			}		
			int other = A.length - small - large;
//			System.out.println(small+" "+large+" "+mid+" "+other);
			if(large + other > N / 2){
				left = mid;
			}else{
				right = mid;
			}
		}
//		System.out.println(left+" "+right);
		return left;
	}

	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 i = 0 ; i < N ; ++i){
			A[i] = sc.nextLong();
			B[i] = sc.nextLong();
		}
		if(N % 2 == 1){
			long low = searchLow(A, B);
			long high = searchHigh(A, B);
//			System.out.println(low+" "+high);
			System.out.println((high - low + 1));			
		}else{
			System.out.println(A[-1]);
		}
	}
}