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"
	"fmt"
	"os"
	"sort"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)
var out = bufio.NewWriter(os.Stdout)

func main() {
	sc.Buffer(make([]byte, 0), 1e6) // maxTokenSize
	sc.Split(bufio.ScanWords)
	defer out.Flush()
	/* --- code --- */
	n := nextInt()
	a := make([]int64, n)
	b := make([]int64, n)
	for i := 0; i < n; i++ {
		a[i] = nextInt64()
		b[i] = nextInt64()
	}
	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]
	})

	lower_bound := med(a)
	upper_bound := med(b)
	fmt.Println(upper_bound - lower_bound + 1)

}

func med(arr []int64) int64 {
	l := len(arr)
	if l%2 == 0 {
		return arr[l/2-1] + arr[l/2]
	}
	return arr[(l-1)/2]
}

// -*-*-*-*-*-*-*-*-
// * I/O utilities *
// -*-*-*-*-*-*-*-*-

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}

func nextInt64() int64 {
	a, _ := strconv.ParseInt(next(), 10, 64)
	return a
}

func nextFloat64() float64 {
	a, _ := strconv.ParseFloat(next(), 64)
	return a
}

func nextInts(n int) []int {
	ret := make([]int, n)
	for i := 0; i < n; i++ {
		ret[i] = nextInt()
	}
	return ret
}
func nextFloats(n int) []float64 {
	ret := make([]float64, n)
	for i := 0; i < n; i++ {
		ret[i] = nextFloat64()
	}
	return ret
}
func nextStrings(n int) []string {
	ret := make([]string, n)
	for i := 0; i < n; i++ {
		ret[i] = next()
	}
	return ret
}

func split(s string) []string {
	ret := make([]string, len([]rune(s)))
	for i, v := range []rune(s) {
		ret[i] = string(v)
	}
	return ret
}

// -*-*-*-*-*-*-*-*-
// * tool snippets *
// -*-*-*-*-*-*-*-*-
func duplicate2Int(base [][]int) (ret [][]int) {
	ret = make([][]int, len(base))
	for i, v := range base {
		ret[i] = append([]int{}, v...)
	}
	return
}

func max(a, b int) int {
	return int(max64(int64(a), int64(b)))
}

func max64(a int64, b int64) int64 {
	if a < b {
		return b
	}
	return a
}

func min(a, b int) int {
	return int(min64(int64(a), int64(b)))
}

func min64(a int64, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

// *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
// * math flavor typical theories *
// *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
func gcd(a, b int) int {
	if a > b {
		return gcd(b, a)
	}
	for a != 0 {
		a, b = b%a, a
	}
	return b
}

func pow(a, b int) (ret int) {
	ret = a
	for i := 0; i < b-1; i++ {
		ret *= a
	}
	return
}

func powMod(n, m, mod int) (ret int) {
	ret = 1
	for m > 0 {
		if m&1 == 1 {
			ret *= n
			ret %= mod
		}
		n *= n
		n %= mod
		m >>= 1
	}
	return ret
}