CF1920C.Partitioning the Array

Allen has an array $a_1, a_2,\ldots,a_n$. For every positive integer $k$ that is a divisor of $n$, Allen does the following:

• He partitions the array into $\frac{n}{k}$ disjoint subarrays of length $k$. In other words, he partitions the array into the following subarrays: $$[a_1,a_2,\ldots,a_k],[a_{k+1}, a_{k+2},\ldots,a_{2k}],\ldots,[a_{n-k+1},a_{n-k+2},\ldots,a_{n}]$$
• Allen earns one point if there exists some positive integer $m$ ($m \geq 2$) such that if he replaces every element in the array with its remainder when divided by $m$, then all subarrays will be identical.

Help Allen find the number of points he will earn.

艾伦有一个数组 $a_1, a_2,\ldots,a_n$。对于每一个能整除 $n$ 的正整数 $k$，艾伦执行以下操作：

• 他将该数组划分为 $\frac{n}{k}$ 个互不相交、长度均为 $k$ 的子数组。换言之，他将数组划分为如下子数组：

  $$[a_1,a_2,\ldots,a_k],\,[a_{k+1}, a_{k+2},\ldots,a_{2k}],\,\ldots,\,[a_{n-k+1},a_{n-k+2},\ldots,a_{n}]$$

• 若存在某个正整数 $m$（满足 $m \geq 2$），使得将数组中每个元素替换为其对 $m$ 取模的余数后，所有子数组均完全相同，则艾伦获得 1 分。

请帮助艾伦计算他总共能获得多少分。

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 2\cdot10^5$) — the length of the array $a$.

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

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

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 10^4$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 2\cdot10^5$），表示数组 $a$ 的长度。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2,\ldots, a_n$（$1 \leq a_i \leq n$），表示数组 $a$ 的元素。

保证所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$。

For each test case, output a single integer — the number of points Allen will earn.

对于每个测试用例，输出一个整数——Allen 将获得的分数。

In the first test case, $k=2$ earns a point since Allen can pick $m = 2$ and both subarrays will be equal to $[1, 0]$. $k=4$ also earns a point, since no matter what $m$ Allen chooses, there will be only one subarray and thus all subarrays are equal.

In the second test case, Allen earns $1$ point for $k=3$, where his choice for $m$ does not matter.

在第一个测试用例中，$k=2$ 得 1 分，因为艾伦可以选择 $m = 2$，此时两个子数组均为 $[1, 0]$。$k=4$ 同样得 1 分，因为无论艾伦选择何种 $m$，都只会产生一个子数组，因此所有子数组自然相等。

在第二个测试用例中，艾伦在 $k=3$ 时得 1 分，此时他选择的 $m$ 值无关紧要。