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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)


function Main(input) {
  var N = input.trim();
  var l = N.length;
  N = parseInt(N, 10);
  var ans;
  if (N <= 10 ) {
    ans = Math.min(9, N);
  } else {
    ans = 9;
    var tmpX;
    var tmpY;

    for (var i = 1; i <=9 ;i++){
      for (var j = 1; j<=i; j++){
        if (i == j){
          tmpX = 0;
          basic_loop:
          for (var k = 0; k < (l - 1); k++){
            for (var middle = 0; middle < Math.pow(10, k); middle ++){
              if (i * Math.pow(10, k + 1) + middle * 10 + j <= N) tmpX ++;
              else break basic_loop;
            }
          }
          ans += (tmpX + 1) * (tmpX + 1) - 1;
        } else {
          tmpX = tmpY = 0;
          basic_loop2:
          for (var k = 0; k < (l - 1); k++){
            for (var middle = 0; middle < Math.pow(10, k); middle ++){
              if (i * Math.pow(10, k + 1) + middle * 10 + j <= N) tmpX ++;
              else break basic_loop2;
            }
          }
          basic_loop3:
          for (var k = 0; k < (l - 1); k++){
            for (var middle = 0; middle < Math.pow(10, k); middle ++){
              if (j * Math.pow(10, k + 1) + middle * 10 + i <= N) tmpY ++;
              else break basic_loop3;
            }
          }
          ans += tmpX * tmpY * 2;
        }

      }
    }
  }
  console.log(ans);
}
 
Main(require("fs").readFileSync("/dev/stdin", "utf8"));