Dora and Search

### 题目描述 给定一个长度为 $n$ 的排列 $a$ ，问是否存在正整数 $l,r$ 使得 $a_l,a_r$ 均不为 $a_{l...r}$ 中的最大值或最小值。 ### 输入输出格式 第一行一个正整数 $t$ ，表示数据组数。接下来对于每组数据输入包括两行，第一行一个正整数 $n$ ，第二行 $n$ 个正整数代表排列 $a$ 。\ 对于每组数据，若存在符合要求的 $l,r$ ，输出任意一组。若不存在则输出 $-1$ 。 ### 数据范围 $1\leqslant t \leqslant 10\ 000\ ,\ 1\leqslant \Sigma n \leqslant 200\ 000\ ,\ $ $a$ 是一个排列。

As you know, the girl Dora is always looking for something. This time she was given a permutation, and she wants to find such a subsegment of it that none of the elements at its ends is either the minimum or the maximum of the entire subsegment. More formally, you are asked to find the numbers $ l $ and $ r $ $ (1 \leq l \leq r \leq n) $ such that $ a_l \neq \min(a_l, a_{l + 1}, \ldots, a_r) $ , $ a_l \neq \max(a_l, a_{l + 1}, \ldots, a_r) $ and $ a_r \neq \min(a_l, a_{l + 1}, \ldots, a_r) $ , $ a_r \neq \max(a_l, a_{l + 1}, \ldots, a_r) $ . A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in any order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ occurs twice in the array) and $ [1,3,4] $ is also not a permutation ( $ n=3 $ , but $ 4 $ is present in the array). Help Dora find such a subsegment, or tell her that such a subsegment does not exist.

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. Description of the test cases follows. For each test case, the first line contains one integer $ n $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ ) — the length of permutation. The second line contains $ n $ distinct integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq n $ ) — the elements of permutation. It is guarented that the sum of $ n $ over all test cases doesn't exceed $ 2 \cdot 10^5 $ .

For each test case, output $ -1 $ if the desired subsegment does not exist. Otherwise, output two indexes $ l, r $ such that $ [a_{l}, a_{l + 1}, \ldots, a_{r}] $ satisfies all conditions. If there are several solutions, then output any of them.

4
3
1 2 3
4
2 1 4 3
7
1 3 2 4 6 5 7
6
2 3 6 5 4 1

-1
1 4
2 6
-1

In the first and fourth test cases, it can be shown that there are no desired subsegments. In the second test case, the subsegment $ [1, 4] $ satisfies all the conditions, because $ \max(a_1, a_2, a_3, a_4) = 4, \min(a_1, a_2, a_3, a_4) = 1 $ , as we see, all the conditions are met. In the third test case, the subsegment $ [2, 6] $ also satisfies all the conditions described.