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: Wrong Answer)

#include <stdio.h>
//#include <stdlib.h>
//#include <string.h>
//#include <stdbool.h>
//#include <limits.h>
//#include <math.h>

int main() {
  int n;
  scanf("%d", &n);
  int ans = 0, cnt = 0, dig = 1, fn, m = n, a[9][9] = {0};
  while (m != 0) {
    cnt++;
    dig *= 10;
    m /= 10;
  }
  dig /= 10;
  fn = n/dig;
  if (cnt > 2) {
    int t = 1;
    for (int i=0; i<9; i++) a[i][i]++;
    for (int i=1; i<cnt-1; i++) {
      for (int j=0; j<9; j++) {
        for (int k=0; k<9; k++) {
          a[i][j] += t;
        }
      }
      t *= 10;
    }
    for (int i=1; i<fn; i++) {
      for (int j=0; j<9; j++) {
        a[i-1][j] += dig/10;
      }
    }
    for (int i=0; i<9; i++) {
      if (n >= fn*dig + i+1)
        a[fn-1][i] += (n - (fn * dig + i+1))/10 +1;
    }
  } else {
    for (int i=0; i<9; i++) {
      if (i+1 <= n) a[i][i]++;
      for (int j=0; j<9; j++) {
        if ((i+1)*10+j+1 <= n) a[i][j]++;
      }
    }
  }
  for (int i=0; i<9; i++) {
    for (int j=0; j<9; j++) {
      ans += a[i][j]*a[j][i];
    }
  }
  printf("%d\n", ans);
  return 0;
}