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(dead_code)]
fn is_whitespace(c: &char) -> bool {
    c.is_whitespace()
}

#[allow(dead_code)]
fn is_eol(c: &char) -> bool {
    ['\r', '\n'].contains(c)
}

#[allow(unused_macros)]
macro_rules! input {
    ($var:ident, $($r:tt)*) => {
        input_inner!{$var, $($r)*}
    };

    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        #[allow(unused_mut, unused_variables, bare_trait_objects)]
        let mut next = move |f: &Fn(&char)->bool| -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|f(&c))
                .take_while(|c|!f(&c))
                .collect()
        };
        input_inner!{next, $($r)*};
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; eol ]) => {
        $next(&is_eol).split(' ').map(|x| x.parse::<$t>().unwrap()).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, parser) => {
        $next
    };

    ($next:expr, $t:ty) => {
        $next(&is_whitespace).parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap, HashSet};

#[allow(dead_code)]
struct Edge {
    from: usize,
    to: usize,
}

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;
#[allow(dead_code)]
const M: usize = 1_000_000_007;

use std::cmp::Ordering;
trait BinarySearch<T> {
    fn upper_bound(&self, value: &T) -> Option<usize>;
    fn lower_bound(&self, value: &T) -> Option<usize>;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn upper_bound(&self, value: &T) -> Option<usize> {
        let (mut ng, mut ok) = (-1, self.len() as isize);
        while (ok - ng).abs() > 1 {
            let mid = ((ok + ng) / 2) as usize;
            match value.cmp(&self[mid]) {
                // v < mid
                Ordering::Less => {
                    ok = mid as isize;
                }
                Ordering::Equal | Ordering::Greater => {
                    ng = mid as isize;
                }
            };
        }
        if ok >= 0 && ok < self.len() as isize {
            Some(ok as usize)
        } else {
            None
        }
    }

    fn lower_bound(&self, value: &T) -> Option<usize> {
        let (mut ng, mut ok) = (-1, self.len() as isize);
        while (ok - ng).abs() > 1 {
            let mid = ((ok + ng) / 2) as usize;
            match value.cmp(&self[mid]) {
                // v <= mid
                Ordering::Less | Ordering::Equal => {
                    ok = mid as isize;
                }
                Ordering::Greater => {
                    ng = mid as isize;
                }
            };
        }
        if ok >= 0 && ok < self.len() as isize {
            Some(ok as usize)
        } else {
            None
        }
    }
}

fn main() {
    input! {
        n: usize,
        ab: [(usize, usize); n],
    }

    let mut ab = ab
        .into_iter()
        .map(|(a, b)| (a * 2, b * 2))
        .collect::<Vec<_>>();
    ab.sort();

    let mut asort = ab.iter().map(|&(a, _)| a).collect::<Vec<_>>();
    asort.sort();
    let mut bsort = ab.iter().map(|&(_, b)| b).collect::<Vec<_>>();
    bsort.sort();

    if n % 2 == 1 {
        let rmin = asort[n / 2];
        let rmax = bsort[n / 2];
        println!("{}", rmax / 2 - rmin / 2 + 1);
    } else {
        let rmin1 = asort[n / 2 - 1];
        let rmax1 = bsort[n / 2 - 1];
        let rmin2 = asort[n / 2];
        let rmax2 = bsort[n / 2];
        let rmin = (rmin1 + rmin2) / 2;
        let rmax = (rmax1 + rmax2) / 2;
        println!("{}", rmax - rmin + 1);
    }
}