Task: Data-transform-reshape (source dataset: Auto-Tables)

Given a table, predict what python pandas transformation may be needed on the given input table. Valid choices for transformation include: {"stack", "wide_to_long", "transpose", "pivot", "explode", "ffill", "subtitles"}. Note that each of these is a common Python Pandas operator. Some transformations can have parameters. Each transformation and its parameters are describe as follows.
 
- stack: collapse homogeneous cols into rows.
@param (int): stack_start_idx: zero-based starting column index of the homogeneous column-group.
@param (int): stack_end_idx: zero-based ending column index of the homogeneous column-group.
 
- wide_to_long: collapse repeating col-groups into rows.
@param (int): wide_to_long_start_idx: zero-based starting column index of the repeating col-groups.
@param (int): wide_to_long_end_idx: zero-based ending column index of the repeating col-groups.
 
- transpose: convert rows to columns and vice versa.
 
- pivot: pivot repeating row-groups into cols.
@param (int): pivot_row_frequency: frequency of repeating row-groups.
 
- ffill: fill structurally empty cells in tables.
@param (int): ffill_end_idx: zero-based ending column index of the columns to be filled.
 
- explode: convert composite cells into atomic values
@param (int): explode_column_idx: zero-based column index of the column to be exploded.
 
- subtitle: convert table subtitles into a column.
 
OUTPUT the predicted transformation name along with its parameters for the given INPUT table in a JSON, e.g., {"transformation": "stack", "stack_start_idx": 1, "stack_end_idx": 5}. If the input table needs multi-step transformations (e.g, ffill followed by stack), list JSON of each transformation sequentially in a list, e.g., [{"transformation": "ffill", "ffill_end_idx": 1}, {"transformation": "stack", "stack_start_idx": 1, "stack_end_idx": 5}]. No explanation is needed.

## Input:
|   year |   day |       1 |       2 |       3 |       4 |       5 |       6 |       7 |       8 |       9 |      10 |      11 |      12 |
|-------:|------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|
|   1964 |     1 | 174.225 | 160.805 | 117.887 | 195.758 | 152.533 | 103.144 | 129.001 | 112.53  | 104.264 | 188.528 | 163.551 | 167.536 |
|   1964 |     2 | 149.364 | 131.37  | 118.691 | 135.321 | 148.275 | 160.51  | 101.694 | 128.972 | 108.902 | 104.507 | 155.93  | 138.992 |
|   1964 |     3 | 165.34  | 181.931 | 167.297 | 133.615 | 154.269 | 148.869 | 119.085 | 167.829 | 197.556 | 147.61  | 150.857 | 137.333 |
|   1964 |     4 | 106.954 | 182.973 | 131.468 | 170.268 | 154.001 | 124.572 | 103.815 | 140.504 | 119.535 | 169.045 | 147.538 | 109.905 |
|   1964 |     5 | 154.725 | 143.555 | 101.442 | 127.977 | 180.676 | 132.019 | 106.744 | 121.696 | 154.323 | 198.529 | 178.391 | 102.876 |
|   1964 |     6 | 104.524 | 193.783 | 144.944 | 162.019 | 158.917 | 104.344 | 101.809 | 154.761 | 184.352 | 122.53  | 142.228 | 126.932 |
|   1964 |     7 | 171.732 | 191.604 | 186.276 | 148.875 | 182.144 | 118.635 | 148.333 | 156.233 | 106.683 | 116.958 | 171.177 | 154.688 |
|   1964 |     8 | 197.244 | 176.654 | 111.677 | 121.184 | 140.657 | 130.003 | 160.538 | 125.846 | 193.173 | 125.129 | 122.398 | 190.813 |
|   1964 |     9 | 110.676 | 159.536 | 100.39  | 177.563 | 195.586 | 135.769 | 190.91  | 149.22  | 188.87  | 185.477 | 150.433 | 172.188 |
|   1964 |    10 | 179.992 | 135.597 | 185.474 | 123.579 | 168.539 | 197.208 | 194.367 | 151.47  | 128.745 | 116.842 | 132.131 | 129.978 |
|   1964 |    11 | 150.192 | 161.011 | 195.5   | 135.381 | 122.587 | 199.544 | 184.023 | 126.413 | 142.976 | 173.179 | 178.737 | 125.129 |
|   1964 |    12 | 127.327 | 154.962 | 122.687 | 145.507 | 173.997 | 107.268 | 103.708 | 165.922 | 128.713 | 133.791 | 115.534 | 140.587 |
|   1964 |    13 | 143.233 | 168.691 | 195.187 | 164.565 | 187.739 | 121.107 | 196.737 | 180.964 | 186.917 | 179.546 | 102.135 | 174.253 |
|   1964 |    14 | 156.682 | 122.527 | 161.453 | 145.792 | 165.516 | 123.382 | 133.139 | 132.985 | 170.724 | 175.423 | 178.314 | 196.283 |
|   1964 |    15 | 153.477 | 188.413 | 182.904 | 155.727 | 144.521 | 198.08  | 197.428 | 182.572 | 171.116 | 150.785 | 179.987 | 133.283 |
|   1964 |    16 | 188.37  | 107.323 | 148.879 | 176.256 | 149.03  | 134.071 | 175.652 | 154.498 | 184.006 | 168.572 | 130.765 | 152.212 |
|   1964 |    17 | 136.263 | 192.645 | 175.07  | 176.852 | 157.356 | 131.59  | 191.043 | 168.328 | 167.563 | 191.923 | 126.168 | 178.867 |
|   1964 |    18 | 134.669 | 196.439 | 116.403 | 113.083 | 131.152 | 119.333 | 156.248 | 128.802 | 118.458 | 130.302 | 135.268 | 192.644 |
|   1964 |    19 | 157.501 | 178.605 | 125.843 | 194.534 | 159.379 | 153.757 | 120.868 | 186.503 | 108.749 | 137.945 | 167.037 | 171.081 |
|   1964 |    20 | 113.83  | 156.922 | 193.283 | 107.491 | 131.21  | 157.468 | 191.049 | 187.516 | 176.099 | 170.96  | 123.363 | 181.081 |
|   1964 |    21 | 198.382 | 192.926 | 133.359 | 134.347 | 129.198 | 129.115 | 154.021 | 196.394 | 170.639 | 108.475 | 143.869 | 118.438 |
|   1964 |    22 | 184.786 | 175.638 | 107.608 | 127.893 | 186.404 | 104.308 | 159.17  | 114.847 | 182.3   | 110.537 | 148.856 | 195.908 |
|   1964 |    23 | 193.218 | 144.777 | 130.542 | 107.368 | 195.79  | 196.259 | 102.182 | 122.5   | 129.355 | 182.614 | 108.064 | 115.346 |
|   1964 |    24 | 131.941 | 105.826 | 111.988 | 152.637 | 129.07  | 144.563 | 176.279 | 110.821 | 157.779 | 118.44  | 102.771 | 168.843 |
|   1964 |    25 | 129.085 | 118.392 | 185.18  | 195.641 | 101.749 | 182.08  | 139.238 | 193.641 | 160.19  | 117.216 | 130.462 | 115.985 |
|   1964 |    26 | 106.871 | 157.646 | 122.578 | 110.124 | 159.694 | 110.616 | 120.564 | 151.74  | 118.112 | 187.956 | 181.883 | 199.385 |
|   1964 |    27 | 137.781 | 129.413 | 130.796 | 101.414 | 192.404 | 146.691 | 122.401 | 116.138 | 167.125 | 155.963 | 169.642 | 127.83  |
|   1964 |    28 | 131.037 | 132.793 | 199.734 | 137.375 | 153.262 | 168.805 | 157.769 | 138.534 | 110.331 | 157.627 | 176.498 | 117.351 |
|   1964 |    29 | 113.673 | 125.261 | 114.912 | 111.691 | 191.791 | 113.819 | 193.498 | 128.451 | 168.508 | 175.367 | 125.512 | 165.485 |
|   1964 |    30 | 167.423 | 188.887 | 162.744 | 103.23  | 123.1   | 103.957 | 159.782 | 190.723 | 157.867 | 129.9   | 168.647 | 121.402 |

## Output:


source: stackoverflow
label: operator: stack
stack_start_idx: 2
stack_end_idx: 13