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: Accepted)

const inputs = require('fs')
  .readFileSync('/dev/stdin', 'utf8')
  .trim()
  .split(/\s+/)

const N = parseInt(inputs[0])
const A = new Array(N)
const B = new Array(N)

for (let i = 0, p = 1; i < N; i += 1) {
  A[i] = parseInt(inputs[p++])
  B[i] = parseInt(inputs[p++])
}

const cmp = (a, b) => a - b
A.sort(cmp)
B.sort(cmp)

if (N % 2 == 0) { // even
  const i1 = N / 2 - 1
  const i2 = N / 2
  const maxMed = B[i1] + B[i2]
  const minMed = A[i1] + A[i2]
  console.log(maxMed - minMed + 1)
} else { // odd
  const i = (N - 1) / 2
  const maxMed = B[i]
  const minMed = A[i]
  console.log(maxMed - minMed + 1)
}