SP5161 FACVSPOW - Factorial vs Power

Consider two integer sequences **f(n) = n!** and **g(n) = a $ ^{n} $** , where **n** is a positive integer. For any integer **a > 1** the second sequence is greater than the first for a finite number of values. But starting from some integer **k**, **f(n)** is greater than **g(n)** for all **n >= k**. You are to find the least positive value of **n** for which **f(n) > g(n)**, for a given positive integer **a > 1**.

The first line of the input contains number **t** – the amount of tests. Then **t** test descriptions follow. Each test consist of a single number **a**.

For each test print the least positive value of **n** for which **f(n) > g(n)**.