Minimize Permutation Subarrays
You 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.
For 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.
The 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 $$$2\cdot 10^5$$$.
For 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.
for s in [*open(0)][2::2]:
    a = s.split()
    a = (*map(a.index, (*'12', str(len(a)))),)
    print(a[2] + 1, sorted(a)[1] + 1)
for s in [*open(0)][2::2]:
    a = s.split()
    a = (*map(a.index, (*'12', str(len(a)))),)
    print(a[2] + 1, sorted(a)[1] + 1)
for v in [*open(0)][2::2]:
    a = v.split()
    a = (*map(a.index, (*'12', str(len(a)))),)
    print(a[2] + 1, sorted(a)[1] + 1)