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: Accepted)

program handstand2
  implicit none
  integer :: n, i, a, b
  integer(8) :: c(9,9) = 0, x = 0
  read(*,*) n
  do i = 1, n
    a = mod(i,10)
    if (a == 0) cycle
    b = i
    do while (b >= 10)
      b = b/10
    end do
    c(a,b) = c(a,b)+1
  end do
  do a = 1, 9
    do b = 1, 9
      x = x+c(a,b)*c(b,a)
    end do
  end do
  write(*,'(i0)') x
end program handstand2