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"
)

func main() {
	var n int
	fmt.Scanf("%d", &n)

	counter := 0
	for a := 1; a <= 9; a++ {
		for b := 1; b <= 9; b++ {
			counter += count(n, a, b) * count(n, b, a)
		}
	}

	fmt.Printf("%d\n", counter)
}

func count(bound, l, r int) int {
	c := 0
	for i := 1; i <= bound; i++ {
		t := i
		for t >= 10 {
			t /= 10
		}
		if t == l && i%10 == r {
			c++
		}
	}
	return c
}