A number is called **n**-factorful if it has exactly **n** distinct prime
factors. Given positive integers **a**, **b**, and **n**, your task is to find
the number of integers between **a** and **b**, inclusive, that are
**n**-factorful. We consider 1 to be 0-factorful.  
  

## Input

Your input will consist of a single integer **T** followed by a newline and
**T** test cases. Each test cases consists of a single line containing
integers **a**, **b**, and **n** as described above.  
  

## Output

Output for each test case one line containing the number of **n**-factorful
integers in [**a**, **b**].  
  

## Constraints

**T** = 20  
1 ≤ **a** ≤ **b** ≤ 107  
0 ≤ **n** ≤ 10