Problem Statement

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 $10^9 + 7$.

Constraints

• $1 \leq S \leq 10^8$

Input

Input is given from Standard Input in the following format:

S

Output

Print the answer.