Product of Array Except Self

Given an array of integers, compute a new array result such that each element result[i] is equal to the product of all the elements in the original array except nums[i]. The solution must be implemented without using the division operator.

The mathematical formulation is given by:

$$result[i] = \prod_{\substack{j=0 \\ j \neq i}}^{n-1} nums[j] $$

Handle edge cases where the array might be empty or contains a single element. In the case of a single-element array, output 1 as the product of no elements is considered to be 1.

inputFormat

The input is given through standard input (stdin). The first line contains a non-negative integer n (0 ≤ n ≤ 10⁵) representing the number of elements in the array. The second line contains n space-separated integers.

outputFormat

Output a single line to standard output (stdout) containing n space-separated integers, where each integer corresponds to the product of all elements in the input array except the element at that index.

## sample

4
1 2 3 4

24 12 8 6