CF2034D Darius' Wisdom

[Darius the Great](https://en.wikipedia.org/wiki/Darius_the_Great) is constructing $ n $ stone columns, each consisting of a base and between $ 0 $ , $ 1 $ , or $ 2 $ inscription pieces stacked on top. In each move, Darius can choose two columns $ u $ and $ v $ such that the difference in the number of inscriptions between these columns is exactly $ 1 $ , and transfer one inscription from the column with more inscriptions to the other one. It is guaranteed that at least one column contains exactly $ 1 $ inscription. Since beauty is the main pillar of historical buildings, Darius wants the columns to have ascending heights. To avoid excessive workers' efforts, he asks you to plan a sequence of at most $ n $ moves to arrange the columns in non-decreasing order based on the number of inscriptions. Minimizing the number of moves is not required.

The first line contains an integer $ t $ — the number of test cases. ( $ 1 \leq t \leq 3000 $ ) The first line of each test case contains an integer $ n $ — the number of stone columns. ( $ 1 \leq n \leq 2 \cdot 10^5 $ ) The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ , where $ a_i \in \{0,1,2\} $ represents the initial number of inscriptions in the $ i $ -th column. It is guaranteed that at least one column has exactly $ 1 $ inscription. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output an integer $ k $ — the number of moves used to sort the columns. ( $ 0 \leq k \leq n $ ) Then, output $ k $ lines, each containing two integers $ u_i $ and $ v_i $ ( $ 1 \leq u_i, v_i \leq n $ ), representing the indices of the columns involved in the $ i $ -th move. During each move, it must hold that $ |a_{u_i} - a_{v_i}| = 1 $ , and one inscription is transferred from the column with more inscriptions to the other. It can be proven that a valid solution always exists under the given constraints.

Columns state in the first test case: - Initial: $ 0, 2, 0, 1 $ - After the first move: $ 0, 1, 0, 2 $ - After the second move: $ 0, 0, 1, 2 $ Columns state in the second test case: - Initial: $ 1, 2, 0 $ - After the first move: $ 0, 2, 1 $ - After the second move: $ 0, 1, 2 $ In the third test case, the column heights are already sorted in ascending order.