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

int main(void){
	int n, i, j;
	int a[10][10];
	memset(a, 0, sizeof(a));
	scanf("%d", &n);
	for(i=1; i<=n; i++){
		j=i;
		int c=j%10;
		while(j>=10) j/=10;
		a[c][j]++;
	}
	long ans = 0;
	for(i=0; i<=9; i++){
		for(j=0; j<=9; j++){
			ans += a[i][j]*a[j][i];
		}
	}
	printf("%ld\n", ans);
}