C+=

题意翻译

### 题意 有三个整数 $a$，$b$ 与 $n$，每一次可以执行以下操作之一： - 将 $a$ 增加 $b$； - 将 $b$ 增加 $a$。 求使得 $a$ 和 $b$ 中**至少**有一个数**严格大于** $n$ **至少**需要操作几次。 ### 输入格式 本题**含有多组数据**。第一行一个整数 $T$，表示数据组数。 接下来 $T$ 行每行三个整数 $a$，$b$ 与 $n$，含义如上所述。 ### 输出格式 对于每组数据一行一个数，表示最小操作次数。 ### 数据范围 - $1 \leq T \leq 100$ - $1 \leq a,b \leq n \leq 10^9$

题目描述

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?

输入输出格式

输入格式

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.

输出格式

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

输入输出样例

输入样例 #1

2
1 2 3
5 4 100

输出样例 #1

2
7

说明

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.