Good Pairs

Description:

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.

Sample Input:

3
3
5 2 7
5
1 4 2 2 3
1
2

Sample Output:

2 3
1 2
1 1

Note:

In the first case, for $$$i = 2$$$ and $$$j = 3$$$ the equality holds true for all $$$k$$$:

• $$$k = 1$$$: $$$|a_2 - a_1| + |a_1 - a_3| = |2 - 5| + |5 - 7| = 5 = |2 - 7| = |a_2-a_3|$$$,
• $$$k = 2$$$: $$$|a_2 - a_2| + |a_2 - a_3| = |2 - 2| + |2 - 7| = 5 = |2 - 7| = |a_2-a_3|$$$,
• $$$k = 3$$$: $$$|a_2 - a_3| + |a_3 - a_3| = |2 - 7| + |7 - 7| = 5 = |2 - 7| = |a_2-a_3|$$$.