[数学题]zju_1526

sheep426

Big Number
Time limit:
10 Seconds   
Memory limit:
32768K   
Total Submit:
4849   
Accepted Submit:
2040   
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.
Input
Input consists of several lines of integer numbers. The first line contains an integer n, which is the number of cases to be tested, followed by n lines, one integer 1 <= n <= 10^7 on each line.

Output
The output contains the number of digits in the factorial of the integers appearing in the input.
Sample Input
2
10
20
Sample Output
7
19
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[ Last edited by sheep426 on 2005-7-25 at 09:32 ]

sheep426

Stirling found the following formula for approximating factorials:

and more precisely,

小康

有公式

sheep426

loga(MN)=logaM + logaN