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?

Leo 开发了一种新的编程语言 C+=。在 C+= 中，整型变量只能通过 += 运算进行修改，该运算将右操作数值加到左操作数变量上。例如，当 a = 2、b = 3 时执行 a += b，a 的值变为 $5$（b 的值不变）。

在 Leo 的一个原型程序中，有两个整型变量 a 和 b，初始值均为正整数。他可以执行任意多次操作 "a += b" 或 "b += a"。Leo 希望测试对大整数的处理能力，因此他希望使 a 或 b 的值严格大于给定值 $n$。他至少需要执行多少次操作？

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.

第一行包含一个整数 $T$（$1 \leq T \leq 100$）—— 测试用例的数量。

接下来的 $T$ 行，每行描述一个测试用例，包含三个整数 $a, b, n$（$1 \leq a, b \leq n \leq 10^9$）—— 分别为变量 $a$ 和 $b$ 的初始值，以及其中某个变量需超过的阈值。

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

对于每个测试用例，输出一个整数——所需的最少操作次数。各答案之间用换行符分隔。

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.

在第一种情况下，我们无法通过一次操作使变量超过 $3$。一种通过两次操作实现该目标的方法是执行两次 “b += a”。