CF1872G.Replace With Product

Given an array $a$ of $n$ positive integers. You need to perform the following operation exactly once:

• Choose $2$ integers $l$ and $r$ ($1 \le l \le r \le n$) and replace the subarray $a[l \ldots r]$ with the single element: the product of all elements in the subarray $(a_l \cdot \ldots \cdot a_r)$.

For example, if an operation with parameters $l = 2, r = 4$ is applied to the array $[5, 4, 3, 2, 1]$, the array will turn into $[5, 24, 1]$.

Your task is to maximize the sum of the array after applying this operation. Find the optimal subarray to apply this operation.

给定一个包含 $n$ 个正整数的数组 $a$。你需要恰好执行一次如下操作：

• 选择两个整数 $l$ 和 $r$（满足 $1 \le l \le r \le n$），并将子数组 $a[l \ldots r]$ 替换为单个元素：该子数组中所有元素的乘积 $(a_l \cdot \ldots \cdot a_r)$。

例如，若对数组 $[5, 4, 3, 2, 1]$ 执行参数为 $l = 2, r = 4$ 的操作，则数组将变为 $[5, 24, 1]$。

你的任务是使执行该操作后的数组元素之和尽可能大。请找出应执行该操作的最优子数组。

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. This is followed by the description of the test cases.

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

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

It is guaranteed that the sum of the values of $n$ for 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 $t$（$1 \le t \le 10^4$），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 $n$（$1 \le n \le 2 \cdot 10^5$），表示数组 $a$ 的长度。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^9$）。

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 $2$ integers $l$ and $r$ ($1 \le l \le r \le n$) — the boundaries of the subarray to be replaced with the product.

If there are multiple solutions, output any of them.

对于每个测试用例，输出 $2$ 个整数 $l$ 和 $r$（$1 \le l \le r \le n$）—— 表示需要被替换为乘积的子数组的边界。

如果存在多个解，输出其中任意一个即可。

In the first test case, after applying the operation with parameters $l = 2, r = 4$, the array $[1, 3, 1, 3]$ turns into $[1, 9]$, with a sum equal to $10$. It is easy to see that by replacing any other segment with a product, the sum will be less than $10$.

In the second test case, after applying the operation with parameters $l = 3, r = 4$, the array $[1, 1, 2, 3]$ turns into $[1, 1, 6]$, with a sum equal to $8$. It is easy to see that by replacing any other segment with a product, the sum will be less than $8$.

In the third test case, it will be optimal to choose any operation with $l = r$, then the sum of the array will remain $5$, and when applying any other operation, the sum of the array will decrease.

在第一个测试用例中，对参数 $l = 2, r = 4$ 执行操作后，数组 $[1, 3, 1, 3]$ 变为 $[1, 9]$，其和为 $10$。容易看出，若将任意其他子段替换为其乘积，所得数组的和均小于 $10$。

在第二个测试用例中，对参数 $l = 3, r = 4$ 执行操作后，数组 $[1, 1, 2, 3]$ 变为 $[1, 1, 6]$，其和为 $8$。容易看出，若将任意其他子段替换为其乘积，所得数组的和均小于 $8$。

在第三个测试用例中，选择任意满足 $l = r$ 的操作是最优的，此时数组的和保持为 $5$；而执行任意其他操作均会使数组的和减小。