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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>

int main(){
	int N;
	int i, j, cnt, max_digit = 1;
	unsigned long c[100]={0};
	unsigned long ans = 0;

	scanf("%d", &N);

	for(cnt=1; cnt<=N; cnt++){
		if(cnt >= max_digit*10){
			max_digit *= 10;
		}
		i = cnt % 10;
		j = cnt / max_digit;
		c[j*10+i]++;
	}

	for(i=1; i<10; i++){
		for(j=1; j<10; j++){
			ans += c[j*10+i] * c[i*10+j];
		}
	}

	printf("%lu", ans);

	return 0;
}