speed up np.searchsorted or improve speed performance in Python

Question

suppose I have a few lists

b_wi=[[1,2,3,4],[6,7,8,9,10,11]] #b_wi is a subset of x
f_wi=[[5,4,2,7,9],[5,4,3,7,2,3,4]]
x=[[1,2,3,4,5,6,7,8,9,2,5,3],[1,24,36,42,35,6,7,8,91,2,5,3]]

the following two are step functions formed by the above lists.

'''
F1 = f_wi[0][0] if x< b_wi[0][0] ;
     f_wi[0][1] if   b_wi[0][0] <=x< b_wi[0][1];
      ...;
     f_wi[0][-1] if x>= b_wi[1][-1]


F2 = f_wi[1][0] if x< b_wi[1][0] ;
     f_wi[1][1] if   b_wi[1][0] <=x< b_wi[1][1];
      ...;
     f_wi[1][-1] if x>= b_wi[1][-1]
'''

Now I want to get max (F1+F2) and the corresponding interval. I did some searching and found this : Evaluate sum of step functions

However, since the length of intervals is not the same for these step functions, I cannot apply the solution in the link directly. Instead, I did this:

import numpy as np
from pandas.core.common import flatten
def func(x,b,f): 
    return f[np.searchsorted(b,x,side='right')]

intval= np.unique(list(flatten(b_wi)))
x=np.concatenate(([-10000],(intval[:-1]+intval[1:])/2,[10000]))  #b_wi is a subset of x. That is why I can use this.
a=np.zeros((len(x)))
for b, f in zip(b_wi,f_wi):
    a=a+ func(x,b,np.asarray(f))
print(a/2)

Now I get can get the maximum of (F1+F2) using

np.amax(a)

and I can get the interval as well.

This is just a simple example I used to illustrate my question. My actual lists are longer than these and there are 100000 step functions. Since I 'flatten' 'b_wi' in order to find the corresponding interval, the length of 'intval' becomes too large. Hence, my method is too slow. Does anyone know how I could speed it up? I feel like I am using the wrong method. Thank you very much.