P13999 [HackerEarth] 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
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题目描述

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.

输入格式

见题面

输出格式

见题面

样例输入
100 45 100 572 78 77 1524 27 75 639 87 77 2968 82 6 60 32 32 863 65 34 394 31 83 519 11 92 218 35 92 340 53 36 3 88 12 35 15 89 43 82 74 1457 29 6 74 93 88 2812 86 3 60 56 32 157 94 93 4048 3 26 25 67 30 137 29 68 283 18 34 527 84 14 536 73 93 2755 18 84 1271 94 21 887 53 75 3682 46 19 603 30 72 1110 4 37 18 12 16 104 34 84 861 43 66 1000 77 37 1747 16 54 541 41 98 2145 19 101 1090 80 46 3459 33 26 129 62 28 325 19 90 1305 42 22 475 50 15 206 21 91 1318 32 5 10 29 96 2130 45 65 329 86 96 2513 44 27 237 24 39 173 92 56 1473 75 48 2393 40 48 803 21 68 410 90 50 2548 63 77 4499 32 20 64 101 4 236 65 98 5849 2 20 1 68 63 4030 71 36 1353 97 74 4705 37 45 1427 66 34 820 50 47 1684 28 78 1848 70 77 1354 5 40 146 18 92 1132 19 59 1030 23 80 844 77 27 636 77 63 2475 44 79 2159 10 28 67 52 54 2362 63 22 1120 29 78 382 42 94 132 74 11 300 67 84 3816 46 11 425 97 87 790 44 81 3324 74 89 4086 50 91 2072 54 5 103 33 84 15 3 24 19 15 97 792 84 14 170 83 11 400 7 6 7 45 100 556 8 25 8 49 73 1957 42 78 2802 8 9 6
样例输出
6695 0 72 1458 708 0 0 0 0 4890 3466 1565 644 2882 0 3259 108 0 670 2 0 0 3 102 0 0 0 0 0 0 144 12 559 959 0 0 350 0 0 0 702 12 51 0 0 169 0 684 0 0 0 0 0 0 297 38 0 656 0 0 19 3 90 0 0 350 0 4 0 0 0 0 0 360 712 0 0 0 14 0 15582 248 168 0 2082 0 0 829 0 8340 10 247 718 160 0 0 337 0 0 108