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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defparameter N (read))
(defparameter matrix
  (make-array '(9 9)))

(defun convert (num)
  (let* ((s-num (write-to-string num))
         (a (aref s-num 0))
         (b (aref s-num (1- (length s-num)))))
        (cons (digit-char-p a)
              (digit-char-p b))))

(defun calc-matrix (num M)
  (loop for i from 1 to num
        if (not (zerop (mod i 10)))
        do (let ((pair (convert i)))
                (incf (aref M 
                            (1- (car pair))
                            (1- (cdr pair)))))
        finally (return M)))

(defun answer (M)
  (loop with a = 0
   		for i from 0 below 9
        do (loop for j from 0 below 9
                 do (setf a (+ a (* (aref M i j)
                                    (aref M j i)))))
        finally (return a)))

(format t "~A" (answer (calc-matrix N matrix)))