Problem: Let us define two functions f and g on positive integer numbers.
f(n) = \text{product of non-zero digits of } n$$$${ g ( n ) = { \begin{cases} n & \quad { \mathrm { i f ~ } } n < 10 \\ g ( f ( n ) ) & \quad { \mathrm { o t h e r w i s e } } \end{cases} } }
You need to process Q queries. In each query, you will be given three integers l, r and k. You need to print the number of integers x between l and r inclusive, such that g(x) = k.
Input Format: The first line of the input contains an integer Q (1 ≤ Q ≤ 2 × 105) representing the number of queries.
Q lines follow, each of which contains 3 integers l, r and k (1 ≤ l ≤ r ≤ 106, 1 ≤ k ≤ 9).
Output Format: For each query, print a single line containing the answer for that query.
Note: In the first example:
- g(33) = 9 as g(33) = g(3 × 3) = g(9) = 9
- g(47) = g(48) = g(60) = g(61) = 6
- There are no such integers between 47 and 55.
- g(4) = g(14) = g(22) = g(27) = g(39) = g(40) = g(41) = g(58) = 4