[Python] How to conditinonally choose which column to backfill over in polars?

I need to backfill a column in a python polars dataframe over one of three possible columns, based on which one matches the non-null cell in the column to be backfilled.

My dataframe looks something like this:

┌─────┬─────┬─────┬─────────┐
│ id1 ┆ id2 ┆ id3 ┆ call_id │
│ --- ┆ --- ┆ --- ┆ --- │
│ i64 ┆ i64 ┆ i64 ┆ i64 │
╞═════╪═════╪═════╪═════════╡
│ 1 ┆ 4 ┆ 9 ┆ null │
│ 1 ┆ 5 ┆ 9 ┆ null │
│ 1 ┆ 5 ┆ 9 ┆ null │
│ 2 ┆ 5 ┆ 9 ┆ null │
│ 2 ┆ 6 ┆ 9 ┆ 2 │
│ 2 ┆ 7 ┆ 10 ┆ null │
│ 3 ┆ 7 ┆ 11 ┆ null │
│ 3 ┆ 7 ┆ 12 ┆ null │
│ 3 ┆ 7 ┆ 13 ┆ 7 │
│ 3 ┆ 8 ┆ 13 ┆ null │
└─────┴─────┴─────┴─────────┘


And I want it to look like this:

┌─────┬─────┬─────┬─────────┐
│ id1 ┆ id2 ┆ id3 ┆ call_id │
│ --- ┆ --- ┆ --- ┆ --- │
│ i64 ┆ i64 ┆ i64 ┆ i64 │
╞═════╪═════╪═════╪═════════╡
│ 1 ┆ 4 ┆ 9 ┆ null │
│ 1 ┆ 5 ┆ 9 ┆ null │
│ 1 ┆ 5 ┆ 9 ┆ null │
│ 2 ┆ 5 ┆ 9 ┆ 2 │
│ 2 ┆ 6 ┆ 9 ┆ 2 │
│ 2 ┆ 7 ┆ 10 ┆ 7 │
│ 3 ┆ 7 ┆ 11 ┆ 7 │
│ 3 ┆ 7 ┆ 12 ┆ 7 │
│ 3 ┆ 7 ┆ 13 ┆ 7 │
│ 3 ┆ 8 ┆ 13 ┆ null │
└─────┴─────┴─────┴─────────┘


If I knew which column matched, I would have used something to the effect of .with_columns(pl.col('call_id').backfill().over('id1'), but for the life of me I can't figure out how to systematically choose which column to backfill over.

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