Problem:
Score : 400 points

Problem Statement

Given is a string S consisting of digits from 1 through 9.

Find the number of pairs of integers (i,j) (1 ≤ i ≤ j ≤ |S|) that satisfy the following condition:

Condition: In base ten, the i-th through j-th characters of S form an integer that is a multiple of 2019.

Constraints

1 ≤ |S| ≤ 200000

S is a string consisting of digits from 1 through 9.

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of pairs of integers (i,j) (1 ≤ i ≤ j ≤ |S|) that satisfy the condition.

Sample Input 1

1817181712114

Sample Output 1

3

Three pairs - (1,5), (5,9), and (9,13) - satisfy the condition.

Sample Input 2

14282668646

Sample Output 2

2

Sample Input 3

2119

Sample Output 3

0

No pairs satisfy the condition.

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

import qualified Data.Vector.Unboxed as VU
import Data.List (tails)

main :: IO ()
main = do
  ds <- map unsafeCharToInt <$> getLine :: IO [Int]
  let
    tailRems :: [Int]
    tailRems = map snd . scanr step (10, 0) $ ds
      where
        step :: Int -> (Int, Int) -> (Int, Int)
        step d (l, d') = (l * 10 `mod` 2019, (d * l + d') `mod` 2019)
    cs :: VU.Vector Int
    cs = count tailRems
  print . VU.sum . VU.map (\k -> k * pred k `div` 2) $ cs

count :: [Int] -> VU.Vector Int
count = VU.accum (+) (VU.replicate 2019 0) . map (flip (,) 1)

unsafeCharToInt :: Char -> Int
unsafeCharToInt c = fromEnum c - 48

readInt :: String -> Int
readInt "" = 0
readInt s = read s