Daily Temperatures

You are given an array of integers representing the daily temperatures. For each day, determine how many days you would have to wait until a warmer temperature occurs. If there is no future day for which this is possible, output 0 for that day.

The solution should be efficient, ideally running in O(n) time complexity using a stack-based approach.

Mathematical Formulation:

For an array \(T\) of length \(n\), compute an array \(A\) such that for each index \(i\):

\[ A_i = \begin{cases} i' - i, & \text{if } T[i'] > T[i] \text{ and } i' \text{ is the smallest such index};\\ 0, & \text{if no such } i' \text{ exists.} \end{cases} \]

inputFormat

The first line of input contains an integer \(n\) — the number of days.

The second line contains \(n\) space-separated integers representing the temperatures for each day.

outputFormat

Output a single line with \(n\) space-separated integers, where the \(i\)-th integer is the number of days you have to wait after the \(i\)-th day to get a warmer temperature. If there is no such day, output 0 for that position.

## sample

8
73 74 75 71 69 72 76 73

1 1 4 2 1 1 0 0