Need help with Python code with best performance

You are given $N$ numbers on a circle, described by an array $A.$ Find the maximum number of neighbouring pairs whose sums are even. One element can belong to only one pair.

Write a function:

def solution$((A)$

that, given an array A consisting of $N$ integers, returns the maximum number of neighbouring pairs whose sums are even.

Examples:

Given $A=[4,2,5,8,7,3,7],$ the function should return $2.$ We can create two pairs with even sums: $(A[0],A[1])$ and $(A[4],A[5]).$ Another way to choose two pairs is: $(A[0],A[1])$ and $(A[5],A[6]).$

Given $A=[14,21,16,35,22],$ the function should return $1.$ There is only one qualifying pair: $(A[0],A[4]).$

Given $A=[5,5,5,5,5,5],$ the function should return $3.$ We can create three pairs: $(A[0],A[5]),(A[1],A[2])$ and $(A[3],A[4]).$

Write an efficient algorithm for the following assumptions:

$N$ is an integer within the range $[1.\mathrm{.}100,000]$;

each element of array $A$ is an integer within the range $0.\mathrm{.}1,000,000,000.$