code javascript: Given numbers on a circle, find the maximum number of neighbouring pairs with an even sum.

Task description

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:

function solution$($A$)$;

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

Examples:

$1.$ 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$[6]).$

$2.$ Given A $=[14,21,16,35,22],$ the function should return $1.$ There is only one qualifying pair: $($A$[0],$ A$[4]).$

$3.$ 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 $[0.\mathrm{.}1,000,000,000].$