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: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func newScanner() *bufio.Scanner {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
	return scanner
}

var sc = newScanner()

func scanInt() int {
	sc.Scan()
	v, _ := strconv.Atoi(sc.Text())
	return v
}

func scanInts(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = scanInt()
	}
	return a
}

func scanString() string {
	if sc.Scan() {
		return sc.Text()
	}
	panic(sc.Err())
}

func main() {
	n := scanInt()
	x, y := make([]int, n), make([]int, n)
	for i := 0; i < n; i++ {
		x[i], y[i] = scanInt(), scanInt()
	}
	answer := possibleMedian(n, x, y)
	fmt.Println(answer)
}

func debug(a ...interface{}) {
	// fmt.Println(a...)
}

func possibleMedian(n int, x, y []int) int {
	if n%2 == 0 {
		mIndex0 := n/2 - 1
		mIndex1 := mIndex0
		x0 := x[mIndex0]
		y0 := y[mIndex0]
		x1 := x[mIndex1]
		y1 := y[mIndex1]
		meds := []float64{}
		for i := x0; i <= y0; i++ {
			for j := x1; j <= y1; j++ {
				med := float64(i+j) / 2
				exists := false
				for k := 0; k < len(meds); k++ {
					if med == meds[k] {
						exists = true
						break
					}
				}
				if !exists {
					meds = append(meds, med)
				}
			}
		}
		debug(meds)
		return len(meds)
	} else {
		mIndex := (n+1)/2 - 1
		xM := x[mIndex]
		yM := y[mIndex]
		return yM - xM + 1
	}
}