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 OCaml (4.10.0) (judge verdict: Accepted)

let s = read_line()
let a = Array.make 2019 0

let rec f i d n ans =
  if i = -1 then ans
  else
    let j = int_of_char s.[i] - int_of_char '0' in
    let n = (j * d + n) mod 2019 in
    let an = a.(n) in
    a.(n) <- an + 1;
    f (i - 1) (10 * d mod 2019) n (ans + an)

let () =
  a.(0) <- 1;
  let l = String.length s - 1 in
  let ans = f l 1 0 0 in
  Printf.printf "%d\n" ans