In many applications very large integers numbers are required. Some of these applications are using keys for secure transmission of data, encryption, etc. In this problem you are given a number, you have to determine the number of digits in the factorial of the number. \InputFile Input consists of several lines of integer numbers. The first line contains an integer \textbf{T}, which is the number of cases to be tested, followed by \textbf{T} lines, one integer \textbf{1} ≤ \textbf{n} ≤ \textbf{10^7} on each line. \OutputFile The output contains the number of digits in the factorial of the integers appearing in the input.