Product Except Self

Given an integer array \(A\) of length \(n\), your task is to compute an output array \(B\) such that each element \(B_i\) is equal to the product of all elements of \(A\) except \(A_i\). Formally, the formula is given by:

$$ B_i = \prod_{\substack{0 \le j < n \\ j \neq i}} A_j $$

The solution should run in \(O(n)\) time without using division. For example, if \(A = [1, 2, 3, 4]\), then \(B = [24, 12, 8, 6]\). The array may be empty or contain a single element (in which case output \(1\) for that element).

inputFormat

The first line contains a single integer \(n\) (\(0 \le n \le 10^5\)), the number of elements in the array. The second line contains \(n\) integers separated by spaces.

outputFormat

Output a single line containing \(n\) integers separated by spaces, where the \(i\)th integer represents the product of all the numbers in the input array except the one at index \(i\).

4
1 2 3 4

24 12 8 6