I have two Dataframes – graph and search with the same schema

Schema for graph:

SCHEMA = {
    START_RANGE: pl.Int64,
    END_RANGE: pl.Int64,
}

Schema for search:

SCHEMA = {
    START: pl.Int64,
    END: pl.Int64,
}

I want to search the graph dataframe.
For every row in search dataframe, I want to find all the rows in the graph dataframe where the START_RANGE and END_RANGE values are strictly within the range of the search dataframe.

How to achieve this using polars only?

Example –

graph = pl.DataFrame(
    {
        "START_RANGE": [1, 10, 20, 30],
        "END_RANGE": [5, 15, 25, 35],
    },
)

search = pl.DataFrame(
    {
        "START": [2, 6, 7],
        "END": [5, 9, 12], 
    },
)

# Expected output

[2,5] in range [1,5]
[6,9] in range [10,15]
[7,12] is not in any range

output = pl.DataFrame(
    {
        "START_RANGE": [1, 10],
        "END_RANGE": [5, 15],
    },
)