Creating a new column by a condition and selecting the maximum value by shift

This is my DataFrame:

import pandas as pddf = pd.DataFrame(    {'a': [10, 20, 30, 400, 50, 60],'b': [897, 9, 33, 4, 55, 65]    })

And this is the output that I want. I want to create column c.

     a    b      c0   10  897    NaN1   20    9  897.02   30   33    NaN3  400    4  400.04   50   55    NaN5   60   65    NaN

These are the steps needed:

a) Find rows that df.a > df.b

b) From the above rows compare the value from a to its previous value from b. If it was more than previous b value, put a in column c otherwise put the previous b.

For example:

a) Rows 1 and 3 met df.a > df.b

b) From row 1, 20 is less than 897 so 897 is chosen. However in row 3, 400 is greater than 33 so it is selected.

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This is what I have tried but it does not work:

df.loc[df.a > df.b, 'c'] = max(df.a, df.b.shift(1))