Given an array of integers, arr, of size n$,$ that represent the frequency of each element, for each element, do exactly one of these operations:

$1.$ Leave the frequency unchanged.

$2.$ Increase the frequency of the element by x$.$

$3.$ Decrease the frequency of the element by y$.$

$4.$ Multiply the frequency of the element by z$.$

Find the maximum number of elements with the same frequency that can be obtained.

Example

X$=1$

y$=1$

z$=3$

n$=4$

arr $=[1,2,4,10]$

frequency.

After these operations, the array is $[3,3,3,10].$ Return $3,$ the number of elements that are equal in

Function Description

Complete the function findMaxFrequency in the editor below.

findMaxFrequency has the following parameters: int x: the value used in the second operation int y: the value used in the third operation

To obtain the maximum number of elements with the same frequency, do these operations.

Values

arr$[0]=1$

Operation Applied

New Value

arr$[1]=2$

$4($Multiply by z$)$

$1*3=3$

arr$[2]=4$

$2($Increase by x$)$

$2+1=3$

arr$[3]=10$

$3($Decrease by Y$)$

$1($Keep unchanged$)$

$4-1=3$

$10$

int z: the value used in the fourth operation int arr$[$i$]$: the frequency of each element to equalize

Returns

int: the maximum number of equal frequencies that can be obtained

Constraints

$1<=$n$<=10^5$

$1<=$ arr$[$i$]<=10^5$

$1<=$x$,$ y $<=10^4$

$1<=$z$<=10^4$

$$ Input Format for Custom Testing

The first line contains an integer x$.$

The next line contains an integer y$.$

The next line contains an integer z$.$

The next line contains an integer n$,$ the size of arr$[$i$]$ Each of the next n lines contains an integer, arr$[$i$].$

test case $0$:

x$=2,$y$=2,$z$=1,$arr$=[10,5,5,2,11],$n$=5$

output$=2$

test case $1$:

x$=2,$y$=2,$z$=2,$arr$=[3,4,6,8],$n$=4$