G. Replace With Product
brute force; greedy; math
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.
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 \(2 \cdot 10^5\).
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.
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.