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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"math"
	"os"
	"sort"
	"strconv"
)

func main() {
	sc := NewScanner(os.Stdin)
	n, _ := sc.NextInt()
	a, b := make([]int, n), make([]int, n)
	for i := 0; i < n; i++ {
		a[i], _ = sc.NextInt()
		b[i], _ = sc.NextInt()
	}
	ans := solve(n, a, b)
	fmt.Println(ans)
}

func solve(n int, a []int, b []int) int {
	sort.Slice(a, func(i, j int) bool { return a[i] < a[j] })
	sort.Slice(b, func(i, j int) bool { return b[i] < b[j] })
	if n%2 == 0 {
		m1 := b[n/2-1] - a[n/2-1] + 1
		m2 := b[n/2] - a[n/2] + 1
		return m1 + m2 - 1
	}
	return b[n/2] - a[n/2] + 1
}

// Scanner is a wrapper of bufio.Scanner which is customized for competitive programing.
type Scanner struct {
	bufio.Scanner
}

// NewScanner is a constructor for Scanner.
func NewScanner(r io.Reader) *Scanner {
	sc := Scanner{*bufio.NewScanner(r)}
	sc.Buffer([]byte{}, math.MaxInt64)
	sc.Split(bufio.ScanWords)
	return &sc
}

// NextInt reads a integer from io stream.
func (sc *Scanner) NextInt() (int, error) {
	if !sc.Scan() {
		return -1, errors.New("failed to scan")
	}
	return strconv.Atoi(sc.Text())
}