Good Pairs
Description
You are given an array $a_1, a_2, \ldots, a_n$ of positive integers. A good pair is a pair of indices $(i, j)$ with $1 \leq i, j \leq n$ such that, for all $1 \leq k \leq n$, the following equality holds:
$$ |a_i - a_k| + |a_k - a_j| = |a_i - a_j|, $$ where $|x|$ denotes the absolute value of $x$.
Find a good pair. Note that $i$ can be equal to $j$.
The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. Description of the test cases follows.
The first line of each test case contains an integer $n$ ($1 \leq n \leq 10^5$) — the length of the array.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) where $a_i$ is the $i$-th element of the array.
The sum of $n$ for all test cases is at most $2 \cdot 10^5$.
For each test case, print a single line with two space-separated indices $i$ and $j$ which form a good pair of the array. The case $i=j$ is allowed. It can be shown that such a pair always exists. If there are multiple good pairs, print any of them.
Input
The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. Description of the test cases follows.
The first line of each test case contains an integer $n$ ($1 \leq n \leq 10^5$) — the length of the array.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) where $a_i$ is the $i$-th element of the array.
The sum of $n$ for all test cases is at most $2 \cdot 10^5$.
Output
For each test case, print a single line with two space-separated indices $i$ and $j$ which form a good pair of the array. The case $i=j$ is allowed. It can be shown that such a pair always exists. If there are multiple good pairs, print any of them.
Samples
3
3
5 2 7
5
1 4 2 2 3
1
2
2 3
1 2
1 1
Note
In the first case, for $i = 2$ and $j = 3$ the equality holds true for all $k$:
- $k = 1$: $|a_2 - a_1| + |a_1 - a_3| = |2 - 5| + |5 - 7| = 5 = |2 - 7| = |a_2-a_3|$,
- $k = 2$: $|a_2 - a_2| + |a_2 - a_3| = |2 - 2| + |2 - 7| = 5 = |2 - 7| = |a_2-a_3|$,
- $k = 3$: $|a_2 - a_3| + |a_3 - a_3| = |2 - 7| + |7 - 7| = 5 = |2 - 7| = |a_2-a_3|$.