Vivek was roaming around in the electronics shop, where he saw a box called as BlackBox. He was intrigued by its function, so he bought it. It's functionality states that for given integer input N \( \le 1000 \) - it outputs the sum of all the digits in factorial of N (N).
Now Vivek wants to extend its functionality for large numbers. So, he wants you to write a program that can check the correctness of the BlackBox .
INPUT :
The first line of the input contains a single integer T ( the number of test cases ). Next T lines of input contains an integer N .
OUTPUT :
For each test case, print the sum of all digits in the factorial of the corresponding input integer.
CONSTRAINTS :
\(1 \le T \le 10^3\)
\(0 \le N \le 1000\)
5 1 2 3 4 5
1 2 6 6 3
for test 1, \(N=1\) , factorial of \(N = 1\) , sum of digits = 1. for test 2, \(N=2\) , factorial of \(N = 2\) , sum of digits = 2. for test 3, \(N=3\) , factorial of \(N = 6\) , sum of digits = 6. for test 4, \(N=4\) , factorial of \(N = 24\) , sum of digits = 6. for test 5, \(N=5\) , factorial of \(N = 120\) , sum of digits = 3.
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