CF1042C.Array Product

You are given an array $a$ consisting of $n$ integers. You can perform the following operations with it:

1. Choose some positions $i$ and $j$ ($1 \le i, j \le n, i \ne j$), write the value of $a_i \cdot a_j$ into the $j$-th cell and remove the number from the $i$-th cell;
2. Choose some position $i$ and remove the number from the $i$-th cell (this operation can be performed no more than once and at any point of time, not necessarily in the beginning).

The number of elements decreases by one after each operation. However, the indexing of positions stays the same. Deleted numbers can't be used in the later operations.

Your task is to perform exactly $n - 1$ operations with the array in such a way that the only number that remains in the array is maximum possible. This number can be rather large, so instead of printing it you need to print any sequence of operations which leads to this maximum number. Read the output format to understand what exactly you need to print.

给你一个包含 $n$ 个整数的数组 $a$。你可以对它执行以下操作：

1. 选择两个位置 $i$ 和 $j$（满足 $1 \le i, j \le n$ 且 $i \ne j$），将 $a_i \cdot a_j$ 的值写入第 $j$ 个位置，并从第 $i$ 个位置删除该数；
2. 选择某个位置 $i$，并从第 $i$ 个位置删除该数（该操作最多只能执行一次，且可在任意时刻执行，不一定在开始时）。

每次操作后，数组中元素的个数减少一个。但各位置的编号保持不变。已被删除的数在后续操作中不可再使用。

你的任务是恰好执行 $n - 1$ 次操作，使得最终数组中仅剩的一个数尽可能大。这个数可能非常大，因此你无需输出该数本身，而只需输出任意一个能达成该最大值的操作序列。请参阅输出格式以明确你需要输出的具体内容。

The first line contains a single integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the number of elements in the array.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($-10^9 \le a_i \le 10^9$) — the elements of the array.

第一行包含一个整数 $n$（$2 \le n \le 2 \cdot 10^5$）—— 表示数组中元素的个数。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$-10^9 \le a_i \le 10^9$）—— 表示数组的元素。

Print $n - 1$ lines. The $k$-th line should contain one of the two possible operations.

The operation of the first type should look like this: $1~ i_k~ j_k$, where $1$ is the type of operation, $i_k$ and $j_k$ are the positions of the chosen elements.

The operation of the second type should look like this: $2~ i_k$, where $2$ is the type of operation, $i_k$ is the position of the chosen element. Note that there should be no more than one such operation.

If there are multiple possible sequences of operations leading to the maximum number — print any of them.

输出 $n - 1$ 行。第 $k$ 行应包含以下两种操作之一。

第一类操作的格式为：$1~ i_k~ j_k$，其中 $1$ 表示操作类型，$i_k$ 和 $j_k$ 是所选元素的位置。

第二类操作的格式为：$2~ i_k$，其中 $2$ 表示操作类型，$i_k$ 是所选元素的位置。注意：此类操作至多只能出现一次。

若存在多种可能的操作序列均可达到最大值，则输出任意一种即可。

Let X be the removed number in the array. Let's take a look at all the examples:

The first example has, for example, the following sequence of transformations of the array: $[5, -2, 0, 1, -3] \to [5, -2, X, 1, -3] \to [X, -10, X, 1, -3] \to$ $[X, X, X, -10, -3] \to [X, X, X, X, 30]$. Thus, the maximum answer is $30$. Note, that other sequences that lead to the answer $30$ are also correct.

The second example has, for example, the following sequence of transformations of the array: $[5, 2, 0, 4, 0] \to [5, 2, X, 4, 0] \to [5, 2, X, 4, X] \to [X, 10, X, 4, X] \to$ $[X, X, X, 40, X]$. The following answer is also allowed:

1 5 3
1 4 2
1 2 1
2 3

Then the sequence of transformations of the array will look like this: $[5, 2, 0, 4, 0] \to [5, 2, 0, 4, X] \to [5, 8, 0, X, X] \to [40, X, 0, X, X] \to$ $[40, X, X, X, X]$.

The third example can have the following sequence of transformations of the array: $[2, -1] \to [2, X]$.

The fourth example can have the following sequence of transformations of the array: $[0, -10, 0, 0] \to [X, 0, 0, 0] \to [X, X, 0, 0] \to [X, X, X, 0]$.

The fifth example can have the following sequence of transformations of the array: $[0, 0, 0, 0] \to [X, 0, 0, 0] \to [X, X, 0, 0] \to [X, X, X, 0]$.

设 $X$ 为数组中被移除的数。我们来看所有示例：

第一个示例中，数组变换序列例如如下：$[5, -2, 0, 1, -3] \to [5, -2, X, 1, -3] \to [X, -10, X, 1, -3] \to$ $[X, X, X, -10, -3] \to [X, X, X, X, 30]$。因此，最大答案为 $30$。注意，其他同样能得出答案 $30$ 的变换序列也是正确的。

第二个示例中，数组变换序列例如如下：$[5, 2, 0, 4, 0] \to [5, 2, X, 4, 0] \to [5, 2, X, 4, X] \to [X, 10, X, 4, X] \to$ $[X, X, X, 40, X]$。以下答案也允许：

1 5 3
1 4 2
1 2 1
2 3

此时数组的变换序列为：$[5, 2, 0, 4, 0] \to [5, 2, 0, 4, X] \to [5, 8, 0, X, X] \to [40, X, 0, X, X] \to$ $[40, X, X, X, X]$。

第三个示例中，数组变换序列可为：$[2, -1] \to [2, X]$。

第四个示例中，数组变换序列可为：$[0, -10, 0, 0] \to [X, 0, 0, 0] \to [X, X, 0, 0] \to [X, X, X, 0]$。

第五个示例中，数组变换序列可为：$[0, 0, 0, 0] \to [X, 0, 0, 0] \to [X, X, 0, 0] \to [X, X, X, 0]$。