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)

Scanf.scanf "%s" (fun s ->
    let n = String.length s in
    let arr = Array.make 2019 0 in
    arr.(0) <- 1;
    let rec loop i cur ten =
        if i >= 0 then (
            let cur = (cur + ten * ( int_of_char s.[i] - 48)) mod 2019 in
            arr.(cur) <- arr.(cur) + 1;
            loop (i - 1) cur ((ten * 10) mod 2019)
        )
    in
    loop (n - 1) 0 1;
    Array.fold_left (fun acc v -> acc + v * (v - 1) / 2) 0 arr |> Printf.printf "%d\n"
)