Score : 900 points
For a positive integer n, let us define f(n) as the number of digits in base 10.
You are given an integer S. Count the number of the pairs of positive integers (l, r) (l \leq r) such that f(l) + f(l + 1) + ... + f(r) = S, and find the count modulo 10^9 + 7.
Input is given from Standard Input in the following format:
S
Print the answer.
1
9
There are nine pairs (l, r) that satisfies the condition: (1, 1), (2, 2), ..., (9, 9).
2
98
There are 98 pairs (l, r) that satisfies the condition, such as (1, 2) and (33, 33).
123
460191684
36018
966522825
1000
184984484