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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

"use strict";

function main(arg) {
    const input = arg.trim().split("\n");
    const N = Number(input.shift())
    const A = input.map(x=>Number(x.split(" ")[0]));
    const B = input.map(x=>Number(x.split(" ")[1]));

    let a, b, sum
    if(N%2) {
        const id0 = parseInt((N+1)/2)-1
        a = A[id0]
        b = B[id0]
        sum = b-a+1
    } else {
        const id0 = parseInt(N/2)-1
        const id1 = parseInt(N/2+1)-1
        a = (A[id0] + A[id1])/2
        b = (B[id0] + B[id1])/2
        sum = (b-a)*2+1
    }

    console.log(sum)
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));