{"raw_statement":[{"iden":"problem statement","content":"For a positive integer $n$, let us define $f(n)$ as the number of digits in base $10$.\nYou 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 $10^9 + 7$."},{"iden":"constraints","content":"*   $1 \\leq S \\leq 10^8$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$S$"},{"iden":"sample input 1","content":"1"},{"iden":"sample output 1","content":"9\n\nThere are nine pairs $(l, r)$ that satisfies the condition: $(1, 1)$, $(2, 2)$, $...$, $(9, 9)$."},{"iden":"sample input 2","content":"2"},{"iden":"sample output 2","content":"98\n\nThere are $98$ pairs $(l, r)$ that satisfies the condition, such as $(1, 2)$ and $(33, 33)$."},{"iden":"sample input 3","content":"123"},{"iden":"sample output 3","content":"460191684"},{"iden":"sample input 4","content":"36018"},{"iden":"sample output 4","content":"966522825"},{"iden":"sample input 5","content":"1000"},{"iden":"sample output 5","content":"184984484"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}