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: Time Limit Exceeded)

#include <stdio.h>

int main(void) {
    int n;
    int i, j;
    int t;
    int ans = 0;
    int i_head, i_tail;
    int j_head, j_tail;

    scanf("%d", &n);

    for( i = 1; i <= n; i++) {
        i_tail = i % 10;
        if( i_tail == 0 ) continue;

        for( t = i; t >= 10; t /= 10);
        i_head = t;
        if( i_head == 0 ) continue;

        for( j = i_head; j <= n; j += 10 ) {
            for( t = j; t >= 10; t /= 10);
            j_head = t;

            if( i_tail == j_head ) {
                ans++;
            }
        }
    }

    printf("%d", ans);

    return 0;
}