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 Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(let* ((s (read-line))
       (n (length s))
       (dp (make-array (list (1+ n)) :initial-element 0))
       (c (make-array (list 2019) :initial-element 0))
       (ans 0))
  ;
  (setf (aref c 0) 1)
  ;
  (loop :for i :downfrom (1- n) :to 0
        :do (setf (aref dp i)
                  (mod (+ (aref dp (1+ i))
                          (* (mod (expt 10 (- n i 1)) 2019)
                             (- (char-code (aref s i)) #x30)))
                       2019))
        :do (incf (aref c (aref dp i))))
  (setf ans (loop :for i :from 0 :to 2018
                  :sum (/ (* (aref c i) (1- (aref c i))) 2)))
  (format t "~A~%" ans))