B. Milena and Admirer
time limit per test
1 second
memory limit per test
256 megabytes
standard input
standard output

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.

1 3 2
1 2 3 4
3 2 1
1 4 4 3 5 7 6

In the first test case, Milena can replace the second element of array $$$a$$$ by integers $$$1$$$ and $$$2$$$, so the array would become $$$[\, 1, \, \underline{1}, \, \underline{2}, \, 2 \,]$$$. Only $$$1$$$ operation is required.

In the second test case, the array $$$a$$$ is already non-decreasing, so the answer is $$$0$$$.

In the third test case, Milena can make array $$$a$$$ non-decreasing in $$$3$$$ operations as follows.

  • Select $$$i=1$$$ and $$$x=2$$$ and replace $$$a_1$$$ by $$$2$$$ and $$$1$$$. The array $$$a$$$ becomes equal to $$$[\, \underline{2}, \, \underline{1}, \, 2, \, 1 \, ]$$$.
  • Select $$$i=3$$$ and $$$x=1$$$ and replace $$$a_3$$$ by $$$1$$$ and $$$1$$$. The array $$$a$$$ becomes equal to $$$[\, 2, \, 1, \, \underline{1}, \, \underline{1}, \, 1 \,]$$$.
  • Select $$$i=1$$$ and $$$x=1$$$ and replace $$$a_1$$$ by $$$2$$$ and $$$1$$$. The array $$$a$$$ becomes equal to $$$[\, \underline{1}, \, \underline{1}, \, 1, \, 1, \, 1, \, 1 \,]$$$.

It can be shown that it is impossible to make it non-decreasing in $$$2$$$ or less operations, so the answer is $$$3$$$.