You are given a permutation p of size n. You want to minimize the number of subarrays of p�hat are permutations. In order to do so, you must perform the following operation exactly once:

• Select integers i, j, where 1≤i,j≤n, then
• Swap pi and pj.

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][5,4,1,2,3]. If instead we choose i=j=5, the resulting array will be [5,1,4,2,3][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 (22 appears twice in the array), and [1,3,4] is also not a permutation (n=3 but there is 44 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.

Input

The first line of the input contains a single integer t (1≤t≤104) — 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≤n≤2⋅105) — the size of the permutation.

The next line of each test case contains n integers p1,p2,…pn (1≤pi≤n, all pi are distinct) — the elements of the permutation p.

It is guaranteed that the sum of n over all test cases does not exceed 2⋅1052⋅105.

Output

For each test case, output two integers i and j (1≤i,j≤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

2 3
1 1
5 2
1 4
9 5
8 8
6 10
5 4

Note

For the first test case, there are four possible arrays after the swap:

• If we swap p1 and p2, we get the array [2,1,3][2,1,3], which has 3 subarrays that are permutations ([1][1], [2,1][2,1], [2,1,3][2,1,3]).
• If we swap p1 and p3, we get the array [3,2,1][3,2,1], which has 3 subarrays that are permutations ([1][1], [2,1][2,1], [3,2,1][3,2,1]).
• If we swap p2 and p3, we get the array [1,3,2][1,3,2], which has 2 subarrays that are permutations ([1][1], [1,3,2][1,3,2]).
• If we swap any element with itself, we get the array [1,2,3][1,2,3], which has 3 subarrays that are permutations ([1][1], [1,2][1,2], [1,2,3][1,2,3]).

So the best swap to make is positions 22 and 33.

For the third sample case, after we swap elements at positions 22 and 55, the resulting array is [1,4,2,5,3][1,4,2,5,3]. The only subarrays that are permutations are [1][1] and [1,4,2,5,3][1,4,2,5,3]. We can show that this is minimal.

题意：

给出一个长度为n的排列a，下标为1~n，现在你可以对其中两个位置的数进行交换（且只能交换一次），从而得到b数组，问怎样才可以使b中的所有连续子序列成为排列的个数最少，输出交换的位置。

思路：

我们可以发现，不管怎么交换，我们总会有长度为1的排列和长度为n的排列。

倘若我们要得到长度大于1的排列（假设需要得到长度为k的排列），那么1和2必须得在里面，而且k+1这个数必须不在里面。

所以我们可以直接将n这个数放到1和2之间，这样便是最优情况。

#include<bits/stdc++.h>
using namespace std;
int main()
{int t;cin>>t;while(t--){int a[200001];int n;cin>>n;for(int i=1;i<=n;i++){int x;cin>>x;a[x]=i;}if(a[n]>a[1]&&a[n]>a[2])cout<<a[n]<<" "<<max(a[1],a[2])<<endl;else if(a[n]<a[1]&&a[n]<a[2])cout<<a[n]<<" "<<min(a[1],a[2])<<endl;elsecout<<1<<" "<<1<<endl;}return 0;}