A. C+=time limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputLeo has developed a new programming language C+=. In C+=, integer variables can only be changed with a "+=" operation that adds the right-hand side value to the left-hand side variable. For example, performing "a += b" when a = 2, b = 3 changes the value of a to 5 (the value of b does not change).In a prototype program Leo has two integer variables a and b, initialized with some positive values. He can perform any number of operations "a += b" or "b += a". Leo wants to test handling large integers, so he wants to make the value of either a or b strictly greater than a given value n. What is the smallest number of operations he has to perform?InputThe first line contains a single integer T (1 \leq T \leq 100) — the number of test cases.Each of the following T lines describes a single test case, and contains three integers a, b, n (1 \leq a, b \leq n \leq 10^9) — initial values of a and b, and the value one of the variables has to exceed, respectively.OutputFor each test case print a single integer — the smallest number of operations needed. Separate answers with line breaks.ExampleInput
2
1 2 3
5 4 100
Output
2
7
NoteIn the first case we cannot make a variable exceed 3 in one operation. One way of achieving this in two operations is to perform "b += a" twice.
2
1 2 3
5 4 100

2 7 
['brute force', 'greedy', 'implementation', 'math', '*800']