FCTRL  Factorial
The most important part of a GSM network is so called Base Transceiver Station (BTS). These transceivers form the areas called cells (this term gave the name to the cellular phone) and every phone connects to the BTS with the strongest signal (in a little simplified view). Of course, BTSes need some attention and technicians need to check their function periodically.
ACM technicians faced a very interesting problem recently. Given a set of BTSes to visit, they needed to find the shortest path to visit all of the given points and return back to the central company building. Programmers have spent several months studying this problem but with no results. They were unable to find the solution fast enough. After a long time, one of the programmers found this problem in a conference article. Unfortunately, he found that the problem is so called "Travelling Salesman Problem" and it is very hard to solve. If we have N BTSes to be visited, we can visit them in any order, giving us N! possibilities to examine. The function expressing that number is called factorial and can be computed as a product 1.2.3.4....N. The number is very high even for a relatively small N.
The programmers understood they had no chance to solve the problem. But because they have already received the research grant from the government, they needed to continue with their studies and produce at least some results. So they started to study behaviour of the factorial function.
For example, they defined the function Z. For any positive integer N, Z(N) is the number of zeros at the end of the decimal form of number N!. They noticed that this function never decreases. If we have two numbers N_{1}<N_{2}, then Z(N_{1}) <= Z(N_{2}). It is because we can never "lose" any trailing zero by multiplying by any positive number. We can only get new and new zeros. The function Z is very interesting, so we need a computer program that can determine its value efficiently.
Input
There is a single positive integer T on the first line of input (equal to about 100000). It stands for the number of numbers to follow. Then there are T lines, each containing exactly one positive integer number N, 1 <= N <= 1000000000.
Output
For every number N, output a single line containing the single nonnegative integer Z(N).
Example
Sample Input:
6 3 60 100 1024 23456 8735373
Sample Output:
0 14 24 253 5861 2183837
hide comments
lokesh1729:
20171022 15:27:40
https://brilliant.org/wiki/trailingnumberofzeros/ 

sohailwiiierd:
20171017 10:10:30
HINT :


kuchnahiaata:
20171016 23:01:55
no need of finding factorial ! just learn the concept of trailing zeros from brilliant.org and go for it 

krokkoguy:
20171004 02:16:51
the amount of trailing zeroes is directly proportional to how many 5s there are in n factorial. a good approximation is n/4. 

jaykay12:
20170927 21:04:01
Nice Concept. :D Thanks for the Link :) 

rushikeshkoli:
20170907 12:10:35
thanks for the link..Ac in one go with 0.02 

koko_chef1:
20170829 21:34:21
Why am i getting TLE even when I'm using legendre's formula ?


steevie189:
20170820 08:32:47
thks for the link, awesome formula Last edit: 20170820 18:50:33 

kejriwal_pk:
20170817 20:31:03
Excellent piece of problem. No fancy Algorithm but a bit fancy "Mathematics" 

kholan:
20170806 19:13:29
No need for any fancy algorithms, just think about the numbers which increase the amount of trailing zeroes. Obviously multiples of 10, what else? 
Added by:  adrian 
Date:  20040509 
Time limit:  6s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  ACM Central European Programming Contest, Prague 2000 