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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import qualified Data.Map as M
import Data.Maybe (fromJust)
import Data.Char (intToDigit)

pair::[Char]->(Char,Char)
pair x = (head x,last x)

solve::Int->Int->M.Map (Char,Char) Int->Int
solve i j m = case M.lookup (intToDigit i,intToDigit j) m of
              Just x -> x
              Nothing -> 0

main = do
  n <- readLn
  let hash = M.fromListWith (+) $ map (\x -> (pair x,1)) $ map show [1..n]
  print $ sum [(solve i j hash)*(solve j i hash) | i <- [1..9], j <- [1..9]]