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 itertools::Itertools;
use proconio::{input, marker::*};
use std::cmp::*;
use std::collections::*;
use superslice::*;

fn main() {
    input! {
        n: usize,
        xs: [(u64, u64);n]
    }

    let mut xs_from: Vec<u64> = xs.iter().map(|v| v.0).collect();
    xs_from.sort();

    let mut xs_to: Vec<u64> = xs.iter().map(|v| v.1).collect();
    xs_to.sort();

    let ans = if n % 2 == 1 {
        med(&xs_to) - med(&xs_from) + 1.0
    } else {
        (med(&xs_to) - med(&xs_from)) * 2.0 + 1.0
    };

    println!("{}", ans as u64);
}

fn med(v: &Vec<u64>) -> f64 {
    let n = v.len();
    if n % 2 == 1 {
        v[n / 2] as f64
    } else {
        (v[n / 2] + v[n / 2 - 1]) as f64 / 2.0
    }
}