B. Minimize Permutation Subarraystime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a permutation p of size n. You want to minimize the number of subarrays of p that are permutations. In order to do so, you must perform the following operation exactly once:  Select integers i, j, where 1 \le i, j \le n, then  Swap p_i and p_j. For example, if p = [5, 1, 4, 2, 3] and we choose i = 2, j = 3, the resulting array will be [5, 4, 1, 2, 3]. If instead we choose i = j = 5, the resulting array will be [5, 1, 4, 2, 3].Which choice of i and j will minimize the number of subarrays that are permutations?A permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array), and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).An array a is a subarray of an array b if a can be obtained from b by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.InputThe first line of the input contains a single integer t (1 \le t \le 10^4) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n (3 \le n \le 2\cdot 10^5) — the size of the permutation.The next line of each test case contains n integers p_1, p_2, \ldots p_n (1 \le p_i \le n, all p_i are distinct) — the elements of the permutation p.It is guaranteed that the sum of n over all test cases does not exceed 2\cdot 10^5.OutputFor each test case, output two integers i and j (1 \le i, j \le n)  — the indices to swap in p.If there are multiple solutions, print any of them.ExampleInput
831 2 331 3 251 3 2 5 464 5 6 1 2 398 7 6 3 2 1 4 5 9107 10 5 1 9 8 3 2 6 4108 5 10 9 2 1 3 4 6 7102 3 5 7 10 1 8 6 4 9Output
2 3
1 1
5 2
1 4
9 5
8 8
6 10
5 4
NoteFor the first test case, there are four possible arrays after the swap:   If we swap p_1 and p_2, we get the array [2, 1, 3], which has 3 subarrays that are permutations ([1], [2, 1], [2, 1, 3]).  If we swap p_1 and p_3, we get the array [3, 2, 1], which has 3 subarrays that are permutations ([1], [2, 1], [3, 2, 1]).  If we swap p_2 and p_3, we get the array [1, 3, 2], which has 2 subarrays that are permutations ([1], [1, 3, 2]).  If we swap any element with itself, we get the array [1, 2, 3], which has 3 subarrays that are permutations ([1], [1, 2], [1, 2, 3]).  So the best swap to make is positions 2 and 3.For the third sample case, after we swap elements at positions 2 and 5, the resulting array is [1, 4, 2, 5, 3]. The only subarrays that are permutations are [1] and [1, 4, 2, 5, 3]. We can show that this is minimal.
831 2 331 3 251 3 2 5 464 5 6 1 2 398 7 6 3 2 1 4 5 9107 10 5 1 9 8 3 2 6 4108 5 10 9 2 1 3 4 6 7102 3 5 7 10 1 8 6 4 9
2 3 1 1 5 2 1 4 9 5 8 8 6 10 5 4 
['constructive algorithms', 'math', '*1100']