FUNFACT  Factorial challenge
Ling: Stir, let's go out and play our favorite game.
Stir: I am already having fun with my first factorial program.
Ling: Than I will give you a challenge on factorials. If you fail in it, you will have to come.
Stir: ok..
Ling gives Stir a number x and the challenge is to find the largest value of n such that n! is not greater than the largest value that can be formed by x digits. Stir is stuck with the problem and needs your help. Now, it's your turn to make sure that Stir can continue having fun with factorials.
Input
The first line of the input contains a number t (about 10^5), the number of the test cases. The next t lines contain a number x (1 <= x <= 10^9).
Output
Output a total of t lines with each line containing the value n corresponding to the input case.
Example
Input:
2
1
7
Output:
3
10
hide comments
square1001:
20160726 07:36:49
Oh, I didn't know that Stirling's Approximation is very near to correct answer, but I realized that it is so good. 

Sahil Sharma:
20150110 18:42:26
Wow, a very nice problem. Requires some mathematical knowledge! :) 
Added by:  Siddharth Kothari 
Date:  20100923 
Time limit:  2.412s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  Own problem 