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 Julia (1.4.0) (judge verdict: Accepted)

function Handstand2()
    N = parse(Int, readline())
    C = zeros(Int, 10, 10)
    for n in 1:N
        s = string(n)
        h, t = parse(Int, s[1]), parse(Int, s[end])
        C[h+1, t+1] += 1
    end
    ans = 0
    for i in 1:10
        for j in 1:10
            ans += C[i, j] * C[j, i]
        end
    end
    println(ans)
end
Handstand2()