You are given N fractions, numbered from $0$ to N$-1.$ Your task is to count the number of occurrences of the fraction that appears most often. Notice that two fractions may be equal even if they have different representations; for example, $3/5$ and $6/10$ are equal. You should not assume that floating point operations are precise.

Write a function:

int solution$($vector &X$,$ vector &Y$)$;

that, given two arrays X and Y consisting of N integers each $($which represent the k$-$th fraction as X$[$k$]/$Y$[$k$])$ returns the number of occurrences of the fraction that appears most often.

Examples:

$1.$ Given arrays X $=[1,2,3,4],$ Y $=[2,3,6,8],$ the function should return $3$ as fractions $1/2,3/6,4/8$ are all equal to each other.

$2.$ Given arrays X $=[3,3,4],$ Y $=[5,3,4],$ the function should return $1,$ as no two fractions are equal.

$3.$ Given arrays X $=[4,7,1,2],$ Y $=[2,14,1,2],$ the function should return $2,$ as fractions $1/2$ and $2/4$ are equal.

$4.$ Given arrays X $=[1,2,3,1,2],$ Y $=[2,6,5,1,1],$ the function should return $2,$ as fractions $4/4,4/1,1/2,2/2$ are all equal to each other.

Write an efficient algorithm for the following assumptions:

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

$-$ each element of array X is an integer within the range $[0.\mathrm{.}2,000,000,000]$;

$-$ each element of array Y is an integer within the range $[1.\mathrm{.}2,000,000,000]$;

$-$ arrays X and Y are of equal length.