Big Number

Many applications work with very large numbers. Such applications use large numbers as keys in order to transmit and encrypt data securely.

Given an integer $m$, write a program that computes how many digits $m!$ (m factorial) has, where $m! = 1 \times 2 \times \cdots \times m$.

The first line contains the number of test cases. Each of the following lines contains one integer $m$. ($1 \le m \le 10^7$)

For each test case, print the number of digits of $m!$ (its length in base 10) on its own line.