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 Fortran (gfortran v4.8.4) (judge verdict: Time Limit Exceeded)

program Handstand2

  implicit none

  integer N
  integer a, b
  real logA,logB
  integer intLogA, intLogB
  integer a1, a2, b1, b2
  integer :: count = 0

  read *, N
  do a = 1, N
    do b = 1, N
      logA = log10(real(a))
      logB = log10(real(b))
      intLogA = 10 ** int(logA)
      intLogB = 10 ** int(logB)
      logA = real(intLogA)
      logB = real(intLogB)
      a1 = a / logA
      a2 = mod(a,10)
      b1 = b / logB
      b2 = mod(b,10)
      if (a1 == b2 .and. a2 == b1) then
        ! print *,a,b
        count = count + 1
      end if
    end do
  end do

  print '(i0)', count

end program