CF1656A Good Pairs

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.

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| $ .