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 8.8.3) (judge verdict: Accepted)

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import qualified Data.Vector.Unboxed as VU

main :: IO ()
main = do
  let
    f :: Int -> Int
    f k = 10 * g k + (k `mod` 10)
    g :: Int -> Int
    g k | k < 10    = k
        | otherwise = g (k `div` 10)
    encode :: Int -> Int -> Int
    encode i j = 10 * i + j
  n <- unsafeTextToInt <$> T.getLine :: IO Int
  let
    counts = VU.accum (const . succ) (VU.replicate 100 0) . map (flip (,) () . f) $ [1..n] :: VU.Vector Int
    op :: Int -> Int -> Int
    op i j = counts VU.! encode i j * counts VU.! encode j i
  print . sum $ op <$> [0..9] <*> [0..9]

unsafeTextToInt :: T.Text -> Int
unsafeTextToInt s = case T.signed T.decimal s of
  Right (n, _) -> n
{-# INLINE unsafeTextToInt #-}