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)]
#![allow(dead_code)]
use datastructure::*;
use grapth::*;
use input_scanner::*;
use math::*;
use string_algorithm::*;
use util::*;

use std::cmp;
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, LinkedList, VecDeque};

fn main() {
    let mut scan = Scanner::new();
    let n: usize = scan.next();
    let mut a: Vec<u32> = Vec::with_capacity(n);
    let mut b: Vec<u32> = Vec::with_capacity(n);
    for _i in 0..n {
        let x = scan.next();
        let y = scan.next();
        a.push(x);
        b.push(y);
    }
    a.sort();
    b.sort();

    if n % 2 == 0 {
        println!(
            "{}",
            b[(n - 1) / 2] + b[n / 2] - a[(n - 1) / 2] - a[n / 2] + 1
        );
    } else {
        println!("{}", b[n / 2] - a[n / 2] + 1);
    }
}

mod datastructure {}
mod grapth {}
mod math {}
mod string_algorithm {}
mod util {}
mod input_scanner {
    pub struct Scanner {
        bytes: Vec<u8>,
        begin: usize,
        end: usize,
    }

    impl Scanner {
        pub fn new() -> Self {
            use std::io::Read;
            let mut buffer: Vec<u8> = Vec::new();
            std::io::stdin().read_to_end(&mut buffer).unwrap();
            let end = (0..buffer.len())
                .find(|i| buffer[*i].is_ascii_whitespace())
                .unwrap_or(buffer.len());
            Scanner {
                bytes: buffer,
                begin: 0,
                end: end,
            }
        }
        pub fn next<T: std::str::FromStr>(&mut self) -> T {
            let s: &str =
                unsafe { std::str::from_utf8_unchecked(&self.bytes[self.begin..self.end]) };
            let ret: T = s.parse::<T>().ok().expect("Parse error.");
            self.skip();
            ret
        }
        pub fn next_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
            (0..n).map(|_| self.next()).collect()
        }
        pub fn next_word(&mut self) -> Vec<u8> {
            let r = Vec::from(&self.bytes[self.begin..self.end]);
            self.skip();
            r
        }
        fn skip(&mut self) {
            self.begin = (self.end..self.bytes.len())
                .find(|i| !self.bytes[*i].is_ascii_whitespace())
                .unwrap_or(self.bytes.len());
            self.end = (self.begin..self.bytes.len())
                .find(|i| self.bytes[*i].is_ascii_whitespace())
                .unwrap_or(self.bytes.len());
        }
    }
}