A16318 | Milena and Admirer

Milena has received an array of integers $a_1, a_2, \ldots, a_n$ of length $n$ from a secret admirer. She thinks that making it non-decreasing should help her identify the secret admirer.

She can use the following operation to make this array non-decreasing:

- Select an element $a_i$ of array $a$ and an integer $x$ such that $1 \le x < a_i$ . Then, replace $a_i$ by two elements $x$ and $a_i - x$ in array $a$ . New elements ( $x$ and $a_i - x$ ) are placed in the array $a$ in this order instead of $a_i$ .More formally, let $a_1, a_2, \ldots, a_i, \ldots, a_k$ be an array $a$ before the operation. After the operation, it becomes equal to $a_1, a_2, \ldots, a_{i-1}, x, a_i - x, a_{i+1}, \ldots, a_k$ . Note that the length of $a$ increases by $1$ on each operation.

Milena can perform this operation multiple times (possibly zero). She wants you to determine the minimum number of times she should perform this operation to make array $a$ non-decreasing.

An array $x_1, x_2, \ldots, x_k$ of length $k$ is called non-decreasing if $x_i \le x_{i+1}$ for all $1 \le i < k$ .

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \leq t \leq 10\,000$ ). The description of test cases follows.

The first line of each test case contains a single integer $n$ ( $1\leq n\leq 2\cdot 10^5$ ) — the length of the array $a$ .

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1\leq a_i\leq 10^9$ ) – the array $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ .

For each test case, output one integer — the minimum number of operations required to make the array non-decreasing.

It can be shown that it is always possible to make the array $a$ non-decreasing in the finite number of operations.