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::char::from_digit,
    std::cmp::{max, min},
    std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque},
    std::error::Error,
    std::fmt::Debug,
    std::io::prelude::*,
    std::io::{stdin, stdout, BufReader, BufWriter, Stdin, Stdout, Write},
    std::mem::swap,
    std::str::FromStr,
};
 
type BoxResult<T> = Result<T, Box<dyn std::error::Error>>;


fn main() -> BoxResult<()> {
    let mut scanner = Scanner::new(stdin());
    let n = scanner.read::<usize>()?;
    let mut tops = vec![];
    let mut bottoms = vec![];
    let mut nums = vec![];
    for _ in 0..n {
        let (b, t) = scanner.read_two::<usize, usize>()?;
        tops.push(t);
        bottoms.push(b);
        nums.push(t);
        nums.push(b);
    }
    tops.sort();
    bottoms.sort();
    nums.sort();
    let (mut l1, mut u1) = (0, 0);
    let rank1 = (n + 1) / 2;
    for &x in nums.iter() {
        let c1 = binary_search(x, &tops);
        if c1 >= rank1 {
            break;
        }
        let c2 = binary_search(x + 1, &bottoms);
        if c2 < rank1 {
            continue;
        }
        if l1 == 0 {
            l1 = x;
        }
        u1 = x;
    }
    let (mut l2, mut u2) = (0, 0);
    let rank2 = (n + 2) / 2;
    for &x in nums.iter() {
        let c1 = binary_search(x, &tops);
        if c1 >= rank2 {
            break;
        }
        let c2 = binary_search(x + 1, &bottoms);
        if c2 < rank2 {
            continue;
        }
        if l2 == 0 {
            l2 = x;
        }
        u2 = x;
    }
    if n % 2 == 0 {
        println!("{}", u1 - l1 + 1 + u2 - l2);    
    } else {
        println!("{}", u1 - l1 + 1);
    }
    Ok(())
}

fn binary_search(x: usize, arr: &[usize]) -> usize {
    if arr[0] >= x {
        return 0;
    }
    if arr[arr.len() - 1] < x {
        return arr.len();
    }
    let (mut l, mut r) = (0, arr.len() - 1);
    while r - l > 1 {
        let mid = (l + r) / 2;
        if arr[mid] < x {
            l = mid;
        } else {
            r = mid;
        }
    }
    l + 1
}

pub struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    pub fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    pub fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    pub fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
 
    pub fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    pub fn read_two<T, U>(&mut self) -> BoxResult<(T, U)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            (a, b)
        };
        self.buffer.clear();
        Ok((a, b))
    }
    pub fn read_three<T, U, V>(&mut self) -> BoxResult<(T, U, V)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
        V: FromStr + Copy,
        V::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b, c) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            let c = params[2].parse()?;
            (a, b, c)
        };
        self.buffer.clear();
        Ok((a, b, c))
    }
    pub fn read_four<T, U, V, W>(&mut self) -> BoxResult<(T, U, V, W)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
        V: FromStr + Copy,
        V::Err: Debug + Error + 'static,
        W: FromStr + Copy,
        W::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b, c, d) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            let c = params[2].parse()?;
            let d = params[3].parse()?;
            (a, b, c, d)
        };
        self.buffer.clear();
        Ok((a, b, c, d))
    }
    pub fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    pub fn read_matrix<T>(&mut self, lines: u64) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    pub fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}