CF1854A2.Dual (Hard Version)

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题目描述

Popskyy & tiasu - Dual

The only difference between the two versions of this problem is the constraint on the maximum number of operations. You can make hacks only if all versions of the problem are solved.

You are given an array a1,a2,,ana_1, a_2,\dots, a_n of integers (positive, negative or 00 ). You can perform multiple operations on the array (possibly 00 operations).

In one operation, you choose i,ji, j ( 1i,jn1 \leq i, j \leq n , they can be equal) and set ai:=ai+aja_i := a_i + a_j (i.e., add aja_j to aia_i ).

Make the array non-decreasing (i.e., aiai+1a_i \leq a_{i+1} for 1in11 \leq i \leq n-1 ) in at most 3131 operations. You do not need to minimize the number of operations.

输入格式

Each test contains multiple test cases. The first line contains the number of test cases tt ( 1t5001 \le t \le 500 ). The description of the test cases follows.

The first line contains a single integer nn ( 1n201 \le n \le 20 ) — the length of the array.

The second line contains nn integers a1,a2,,ana_1, a_2, \ldots, a_n ( 20ai20-20 \le a_i \le 20 ) — the array before performing the operations.

输出格式

For each test case, output your operations in the following format.

The first line should contain an integer kk ( 0k310 \le k \le 31 ) — the number of operations.

The next kk lines represent the kk operations in order. Each of these kk lines should contain two integers ii and jj ( 1i,jn1 \leq i, j \leq n ) — the corresponding operation consists in adding aja_j to aia_i .

After all the operations, the array a1,a2,,ana_1, a_2,\dots, a_n must be non-decreasing.

输入输出样例

  • 输入#1

    10
    2
    2 1
    4
    1 2 -10 3
    5
    2 1 1 1 1
    8
    0 0 0 0 0 0 0 0
    5
    1 2 -4 3 -10
    10
    11 12 13 14 15 -15 -16 -17 -18 -19
    7
    1 9 3 -4 -3 -2 -1
    3
    10 9 8
    20
    1 -14 2 -10 6 -5 10 -13 10 7 -14 19 -5 19 1 18 -16 -7 12 8
    20
    -15 -17 -13 8 14 -13 10 -4 11 -4 -16 -6 15 -4 -2 7 -9 5 -5 17

    输出#1

    1
    2 1
    3
    4 4
    4 4
    3 4
    4
    2 1
    3 1
    4 1
    5 1
    0
    7
    3 4
    3 4
    5 4
    5 4
    5 4
    5 4
    5 4
    15
    6 1
    6 1
    6 1
    7 2
    7 2
    7 2
    8 3
    8 3
    8 3
    9 4
    9 4
    9 4
    10 5
    10 5
    10 5
    8
    3 4
    3 4
    2 4
    2 4
    2 4
    2 4
    1 4
    1 4
    3
    2 1
    3 1
    3 1
    31
    14 1
    18 7
    13 11
    15 11
    6 4
    5 17
    19 6
    19 12
    10 5
    11 12
    1 17
    15 19
    16 10
    14 2
    16 11
    20 7
    7 6
    9 5
    3 6
    6 14
    17 18
    18 14
    12 3
    17 16
    8 18
    13 16
    9 8
    14 8
    16 2
    11 8
    12 7
    31
    5 12
    19 13
    9 1
    5 17
    18 19
    6 16
    15 8
    6 9
    15 14
    7 10
    19 7
    17 20
    14 4
    15 20
    4 3
    1 8
    16 12
    16 15
    5 6
    12 10
    11 15
    20 3
    20 19
    13 14
    11 14
    18 10
    7 3
    12 17
    4 7
    13 2
    11 13

说明/提示

In the first test case, by adding a1=2a_1 = 2 to a2a_2 , we get the array [2,3][2, 3] which is non-decreasing.

In the second test case, the array changes as:

  • [1,2,10,3][1, 2, -10, 3]
  • [1,2,10,6][1, 2, -10, 6]
  • [1,2,10,12][1, 2, -10, 12]
  • [1,2,2,12][1, 2, 2, 12]

In the third test case, the final array is [2,3,3,3,3][2, 3, 3, 3, 3] .

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