Pandas dataframe, how to find a very specific max values?

[zljubisic at gmail.com]

I have a dataframe:


df = pd.DataFrame({
   'x': [3,4,5,8,10,11,12,13,15,16,18,21,24,25],
   'a': [10,9,16,4,21,5,3,17,11,5,21,19,3,9]
})

df
Out[30]: 
     a   x
0   10   3
1    9   4
2   16   5
3    4   8
4   21  10
5    5  11
6    3  12
7   17  13
8   11  15
9    5  16
10  21  18
11  19  21
12   3  24


for every "x" value I should subtract a certain number (say 3), and then find a maximum "a" value where x is in a range from x-3 to x.

For example:
index,  x,    x-3,   max(a) where x is between x-3 and x
0, 	3, 	0,	10
1,	4,	1,	10
2,	5,	2,	16
3,	8,	5,	16
4,     10,      7,      21
...	

"x" is incremental, "a" is random
How to find max "a" values?