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: Wrong Answer)

package main

import (
	"fmt"
	"strconv"
)

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

func calc(N, l, r, c int) int {
	// fmt.Println("calc EN: N", N, "l", l, "r", r, "c", c)
	ret := 0
	if l == r {
		t := r
		for N >= t {
			ret++
			t += r * pow(10, ret)
			// fmt.Println("t", t, "r", r)
		}
	} else if c == 2 {
		if r*10+l > N {
			return 0
		}
		return 1
	} else if c >= 3 {
		ret = 10 * (c - 2)
	}
	// fmt.Println("calc EX: ret", ret)
	return ret
}

func main() {
	var N, ans int
	fmt.Scan(&N)
	for i := 1; i <= N; i++ {
		if i%10 == 0 {
			continue
		}
		s := strconv.Itoa(i)
		l := int(s[0] - '0')
		r := int(s[len(s)-1] - '0')
		// fmt.Println("i", i, "l", l, "r", r)
		c, n := 0, N
		for n > 0 {
			c++
			n /= 10
		}
		// 末尾がvでN以下の数の個数は
		ans += calc(N, l, r, c)
	}
	// fmt.Println("ans", ans)
	fmt.Println(ans)
}