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 OCaml (4.02.3) (judge verdict: Time Limit Exceeded)

let n = Scanf.sscanf (read_line ()) "%d" @@ fun n -> n

let f a b =
  if a = 0 then 0
  else begin
    let res = ref 0 in
    for i = 1 to n do
      let t = (int_of_char (string_of_int i).[0]) - 48 in
      if t = a && i mod 10 = b then res := !res + 1
    done;
    !res
  end

let () =
  let ans = ref 0 in
  for i = 0 to 9 do
    for j = 0 to 9 do
      ans := !ans + f i j * f j i
    done
  done;
  Printf.printf "%d\n" !ans