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 (1.14.1) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var N int
	fmt.Scan(&N)
	m := make([][]int, 10)
	for i := 0; i <= 9; i++ {
		m[i] = make([]int, 10)
	}
	for i := 1; i <= N; i++ {
		v := i
		last := i % 10
		first := v % 10
		for v/10 != 0 {
			v /= 10
			first = v % 10
		}
		m[first][last]++
	}
	count := 0
	for i := 1; i <= 9; i++ {
		for j := 1; j <= 9; j++ {
			count += m[i][j] * m[j][i]
		}
	}
	fmt.Println(count)
}