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:
| University (in alphabetical order)   | ARWU (2014)   |   Forbes (2016) |   USNWR (2014) |   Washington Monthly (2014) |
|:-------------------------------------|:--------------|----------------:|---------------:|----------------------------:|
| Brown                                | 43            |               8 |             16 |                         113 |
| Columbia                             | 7             |              16 |              4 |                          51 |
| Cornell                              | 11            |              29 |             15 |                          39 |
| Dartmouth                            | 78–104        |              17 |             11 |                          54 |
| Harvard                              | 1             |               4 |              2 |                          10 |
| Penn                                 | 14            |              11 |              8 |                          41 |
| Princeton                            | 5             |               3 |              1 |                          27 |
| Yale                                 | 9             |               6 |              3 |                          57 |

## Output:


source: web
label: operator: stack
stack_start_idx: 1
stack_end_idx: 4