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)

use proconio::input;

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::ops::*;

#[derive(Clone, Debug, Default)]
struct Struct;

//#[proconio::fastout]
fn main() {
    input! {
        n:usize,
        mut v:[(i64,i64);n],
    }
    let mut vl:Vec<i64> = v.iter().map(|x| x.0).collect();
    let mut vh:Vec<i64> = v.iter().map(|x| x.1).collect();
    vl.sort_unstable();
    vh.sort_unstable_by_key(|x|-x);

    /*
       Nが奇数の時 p=(N-1)/2
         中央値の最小値は vl[p] 最大値は vh[p]

       Nが偶数の時 p1=N/2-1 p1=N/2
         中央値の最小値は (vl[p1]+vl[p2])/2 最大値は (vh[p1]+vh[p2])/2
    */
    let ans;
    if n % 2 == 1 {
        let p = (n-1)/2;
        ans = vh[p]-vl[p]+1;
    } else {
        let p1 = n/2-1;
        let p2 = n/2;
        ans = (vh[p1]+vh[p2]) - (vl[p1]+vl[p2]) + 1;
    }
    println!("{}",ans);

}