CF1368A C+=

Leo 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?

The 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.

For each test case print a single integer — the smallest number of operations needed. Separate answers with line breaks.

In 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.