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))
       (l (length s))
       m)
  (labels ((f (n)
	     (let ((result (assoc n m :test #'=)))
	       (if result
		   (cdr result)
		   (prog1
		       (setf result (loop for x = n then (floor x 10)
				       until (< x 2019)
				       count (zerop (mod x 2019))))
		     (acons n result m))))))
    (if (< l 4)
	(format t "0~%")
	(format t "~d~%"
		(loop for i upto (- (length s) 4)
		   sum (f (parse-integer s :start i)))))))