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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::max;
use std::io;

/*
6
3 10
2 6
10 30
1 3
10 20
8 100
*/
/*
5
3 10
2 6
1 3
10 20
8 100
*/

fn main() {
    let input = input_number();
    let n = input[0] as usize;
    let mut input = (0..n).map(|_| input_number()).collect::<Vec<Vec<i64>>>();

    let median_a: i64;
    input.sort_by(|a, b| a[0].cmp(&b[0]));
    if n % 2 == 0 {
        median_a = input[n / 2][0] + input[n / 2 - 1][0];
    } else {
        median_a = input[n / 2][0];
    }

    let median_b: i64;
    input.sort_by(|a, b| a[1].cmp(&b[1]));
    if n % 2 == 0 {
        median_b = input[n / 2][1] + input[n / 2 - 1][1];
    } else {
        median_b = input[n / 2][1];
    }

    if n % 2 == 0 {
        println!("{}", median_b - median_a + 1);
    } else {
        println!("{}", median_b - median_a + 1);
    }
}

#[allow(dead_code)]
fn update_max<T>(left: &mut T, right: T)
where
    T: std::cmp::Ord + std::clone::Clone,
{
    if *left < right {
        *left = right.clone();
    }
}

#[allow(dead_code)]
fn update_min<T>(left: &mut T, right: T)
where
    T: std::cmp::Ord + std::clone::Clone,
{
    if *left > right {
        *left = right.clone();
    }
}

#[allow(dead_code)]
fn input_number() -> Vec<i64> {
    let mut input = String::new();
    io::stdin()
        .read_line(&mut input)
        .expect("Failed to read line");
    let vec: Vec<i64> = input
        .split_whitespace()
        .map(|x| x.parse().unwrap_or(0))
        .collect();
    vec
}

#[allow(dead_code)]
fn input() -> (u64, f32) {
    let mut s = String::new();
    io::stdin().read_line(&mut s).expect("");
    let mut iter = s.trim().split_whitespace();
    let c: u64 = iter.next().unwrap().parse().unwrap();
    let n: f32 = iter.next().unwrap().parse().unwrap();
    (c, n)
}