possible-rectangles

Sparsh(techno-cultural fest of SVNIT) fever is spread all over SVNIT and now the core-committee of Sparsh wants to propagate it all over the state. The publicity team is planning to fill the nearby places with giant rectangular hoardings. For placing a hoarding they've been given a frame in shape of a grid.

The frame is made up of M rods placed horizontally one above the other and N rods placed vertically on top of the horizontal rods thereby forming a grid. The smallest rectangle formed is a square of unit area.

Now after a while, they are informed only the area of hoarding  (A units) but there isn't any information on it's dimensions. It is also known that the hoarding will be rectangular in shape with integral edge length. 

Now your task is to find how many rectangular frames of different dimensions are possible with area A units in the given grid.
Input:
First line contains single integer denoting number of test cases T.
T lines follows.
Each line contains 3 integers M,N,A.
M,N are two different sizes of rods.
A is area of hoarding.  

Output:
Print single integral answer for each test case in separate lines.

Constraints:
SubTask1:
1 ≤ T ≤ 2500
2 ≤ M,N ≤ 100000
1 ≤ A ≤ (m-1)*(n-1)  

SubTask2: 
1 ≤ T ≤ 25
2 ≤ M,N ≤ 10000000
1 ≤ A ≤ (m-1)*(n-1)  

Problem Setter : Prashant Arya

SAMPLE INPUT
2
2 2 1
4 5 6

SAMPLE OUTPUT
1
7

Explanation

Case 2 : 4 5 6
With the given rods, a grid of 3x4 dimensions can be formed. Now from this, there are 4 different 2x3, and 3 different 3x2 rectangles possible. Thus answer is 7.

Source: hackerearth | Difficulty: UNKNOWN_DIFFICULTY


Solutions: