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.Strict as M
import Data.Maybe

main = do
    n <- readLn :: IO Int
    let ab = M.fromListWith (+) $ map ((\s -> ((head s, last s),1)) . show) [1..n]
        ans = [(fromMaybe 0 (M.lookup (i, j) ab)) * (fromMaybe 0 (M.lookup (j, i) ab))| i <- ['1'..'9'], j <- ['1'..'9']]
    print $ sum ans