$```$

import numpy as np

def binary$\_$search$($sequence$,$ item$\_$to$\_$search$)$:

$\text{'}\text{'}\text{'}$

The code for binary search has been provided. Please modify the code so that

it will return the number of steps it took to find the minimum index of the

number using binary search, given that the number is in the sequence.

In other words, the program should not stop the first time it finds the

number in the sequence, but continue binary search until it finds the minimum

index the number appears at$.$

$>>>$print$($binary$\_$search$([1,1,1,2,3,4],1))$

$2$

$>>>$print$($binary$\_$search$([1,1,1,2,2,2,3,3,4],3))$

$2$

$\text{'}.\text{'}$

low $=0$

high $=$ len$($sequence$)-1$

while low high:

middle $=($low $+$ high$)//2$

if sequence$[$middle$]$ item$\_$to$\_$search:

low $=$ middle $+1$

elif sequence$[$middle$]>$ item$\_$to$\_$search:

high $=$ middle $-1$

else:

return middle

return None

$```$