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 ABC152D
    implicit none
    integer(8)::N,i,j,top,tail
    integer(8)::result=0
    integer(8),dimension(10,10)::C
    read(5,*)N
    C=0

    do i=1,N
        tail=mod(i,10)
        j=i
        top=i
        do
            j=j/10
            if(j==0)then
                exit
            end if
            top=j
        end do
        C(top+1,tail+1)=C(top+1,tail+1)+1
    end do

    do i=1,10
        do j=1,10
            result=result+C(i,j)*C(j,i)
        end do
    end do

    print'(i0)',result
end program ABC152D