Frequency Replacement in a List

Given a list of integers, replace each element of the list with its frequency of occurrence in the original list.

In other words, for each element x in the list, determine how many times x appears and replace that element with that count.

The mathematical formulation of the operation for an element x is given by:

$$ f(x) = \#\{ i \mid a_i = x \} $$

where \(a_i\) refers to the i-th element of the list.

You are required to read the input from standard input and print the output to standard output. The list is given by first an integer n (the number of elements), followed by n integers. The output should be the transformed list, where numbers are separated by a single space.

inputFormat

The first line contains an integer n representing the number of elements in the list.

The second line contains n integers separated by spaces.

outputFormat

Output a single line with n integers where each integer is replaced by its frequency in the original list, separated by a single space.

## sample

5
1 2 3 4 5

1 1 1 1 1