Problem:
Score : 400 points

Problem Statement

Given is a positive integer N.

Find the number of pairs (A, B) of positive integers not greater than N that satisfy the following condition:

When A and B are written in base ten without leading zeros, the last digit of A is equal to the first digit of B, and the first digit of A is equal to the last digit of B.

Constraints

1 \leq N \leq 2 \times 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

25

Sample Output 1

17

The following 17 pairs satisfy the condition: (1,1), (1,11), (2,2), (2,22), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (11,1), (11,11), (12,21), (21,12), (22,2), and (22,22).

Sample Input 2

1

Sample Output 2

1

Sample Input 3

100

Sample Output 3

108

Sample Input 4

2020

Sample Output 4

40812

Sample Input 5

200000

Sample Output 5

400000008

Solution in Go (1.6) (judge verdict: Accepted)

package main

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

var sc = bufio.NewScanner(os.Stdin)

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

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

func max(a, b int) int {
	return int(math.Max(float64(a), float64(b)))
}

func min(a, b int) int {
	return int(math.Min(float64(a), float64(b)))
}

func abs(a, b int) int {
	return int(math.Abs(float64(a) - float64(b)))
}

type pair struct {
	first  int
	second int
}

func intToPair(i int) pair {
	a := i % 10
	iStr := strconv.Itoa(i)
	b := (int)(iStr[0] - '0')
	return pair{
		first:  a,
		second: b,
	}
}

func main() {
	sc.Split(bufio.ScanWords)
	n := nextInt()
	m := make(map[pair]int)

	for i := 1; i <= n; i++ {
		p := intToPair(i)
		m[p]++
	}

	ans := 0
	for i := 0; i <= n; i++ {
		p := intToPair(i)
		q := pair{first: p.second, second: p.first}
		ans += m[q]
	}

	fmt.Print(ans)
}