L. Yet Another Maximize Permutation Subarrays
time limit per test
1.5 s
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a permutation $$$p$$$ of size $$$n$$$. You want to maximize 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 maximize the number of subarrays that are permutations?

NOTE:

  • A permutation of length $$$n$$$ is an array 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 deleting several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input

The first line of the input contains a single integer $$$t\ (1\le t\le 10)$$$ — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n\ (1\le n\le 10^6)$$$ — the size of the permutation.

The next line of each test case contains $$$n$$$ integers $$$p_1,p_2,\cdots p_n$$$ ($$$1\le p_i\le n$$$, all $$$p_i$$$ are distinct) — the elements of the permutation p.

Output

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.

Example
Input
8
3
1 2 3
3
1 3 2
5
1 3 2 5 4
6
4 5 6 1 2 3
9
8 7 6 3 2 1 4 5 9
10
7 10 5 1 9 8 3 2 6 4
10
8 5 10 9 2 1 3 4 6 7
10
2 3 5 7 10 1 8 6 4 9
Output
3 3
1 2
1 4
1 3
9 9
4 9
2 4
1 5