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 (
	"fmt"
	"strconv"
)

func topbottom(x int) (int, int) {
	str := strconv.Itoa(x)
	top, _ := strconv.Atoi(string(str[0]))
	bottom, _ := strconv.Atoi(string(str[len(str)-1]))
	return top, bottom
}
func main() {
	var n int
	fmt.Scan(&n)

	result := 0
	c := [10][10]int{}
	for k := 1; k <= n; k++ {
		top, bottom := topbottom(k)
		c[top][bottom]++
	}
	for i := 0; i <= 9; i++ {
		for j := 0; j <= 9; j++ {
			result += c[i][j] * c[j][i]
		}
	}
	fmt.Println(result)

}