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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var n int
	fmt.Scan(&n)
	a := make([]int, n)
	b := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&a[i], &b[i])
		a[i] *= 2
		b[i] *= 2
	}
	sort.Sort(sort.IntSlice(a))
	sort.Sort(sort.Reverse(sort.IntSlice(b)))

	var ans int
	if n%2 == 1 {
		ans = b[n/2]/2 - a[n/2]/2 + 1
	} else {
		ans = (b[n/2]+b[n/2-1])/2 - (a[n/2]+a[n/2-1])/2 + 1
	}

	fmt.Println(ans)
}