CF1583A.Windblume Ode

A bow adorned with nameless flowers that bears the earnest hopes of an equally nameless person.

You have obtained the elegant bow known as the Windblume Ode. Inscribed in the weapon is an array of $n$ ($n \ge 3$) positive distinct integers (i.e. different, no duplicates are allowed).

Find the largest subset (i.e. having the maximum number of elements) of this array such that its sum is a composite number. A positive integer $x$ is called composite if there exists a positive integer $y$ such that $1 \lt y \lt x$ and $x$ is divisible by $y$.

If there are multiple subsets with this largest size with the composite sum, you can output any of them. It can be proven that under the constraints of the problem such a non-empty subset always exists.

一把装饰着无名花朵的弓，承载着同样无名之人的殷切期望。

你已获得名为「风花颂」的优雅弓箭。该武器上铭刻着一个由 $n$（$n \ge 3$）个互不相同的正整数组成的数组（即所有元素均不同，不允许重复）。

请找出该数组的一个最大子集（即元素个数最多的子集），使得该子集的元素之和为合数。一个正整数 $x$ 被称为合数，当且仅当存在一个正整数 $y$，满足 $1 \lt y \lt x$ 且 $x$ 能被 $y$ 整除。

若存在多个满足上述最大大小且和为合数的子集，你可以输出其中任意一个。在本题约束条件下，可以证明这样的非空子集必然存在。

Each test consists of multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). Description of the test cases follows.

The first line of each test case contains an integer $n$ ($3 \leq n \leq 100$) — the length of the array.

The second line of each test case contains $n$ distinct integers $a_{1},a_{2},\dots,a_{n}$ ($1 \leq a_{i} \leq 200$) — the elements of the array.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 100$）。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 $n$（$3 \leq n \leq 100$）—— 数组的长度。

每个测试用例的第二行包含 $n$ 个互不相同的整数 $a_{1},a_{2},\dots,a_{n}$（$1 \leq a_{i} \leq 200$）—— 数组的元素。

Each test case should have two lines of output.

The first line should contain a single integer $x$: the size of the largest subset with composite sum. The next line should contain $x$ space separated integers representing the indices of the subset of the initial array.

每个测试用例应输出两行。

第一行应包含一个整数 $x$：满足子集元素和为合数的最大子集的大小。
第二行应包含 $x$ 个以空格分隔的整数，表示原数组中该子集的下标。

In the first test case, the subset ${a_2, a_1}$ has a sum of $9$, which is a composite number. The only subset of size $3$ has a prime sum equal to $11$. Note that you could also have selected the subset ${a_1, a_3}$ with sum $8 + 2 = 10$, which is composite as it's divisible by $2$.

In the second test case, the sum of all elements equals to $21$, which is a composite number. Here we simply take the whole array as our subset.

在第一个测试用例中，子集 $\{a_2, a_1\}$ 的和为 $9$，这是一个合数。唯一大小为 $3$ 的子集的和为 $11$，是质数。注意，你也可以选择子集 $\{a_1, a_3\}$，其和为 $8 + 2 = 10$，该数可被 $2$ 整除，因此是合数。

在第二个测试用例中，所有元素的和为 $21$，这是一个合数。此时我们直接取整个数组作为所求子集。