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
rayofhopee:
20160725 15:04:47
print a new line after output(cout<<ans<<endl; or printf("%d\n",ans);. cost me many wrong ans :( 

dristybutola:
20160702 16:15:10
just need to use algorithm for trailing zeroes.Thats it!! Last edit: 20160702 16:18:14 

heemansh:
20160701 16:59:55
how can output of 3 be 14???..


gopal9yedida:
20160629 15:47:08
can anyone help in understanding the last paragraph of description i.e..about Z(N) plz 

mondalsourav:
20160620 00:24:14
solved in 1st attempt :D


mondalsourav:
20160620 00:12:55
How should the program behave when T and N have exceeded their limits??


mkfeuhrer:
20160605 09:31:07
trailing zero's....... AC in 1 go :) 

get_right_jr:
20160531 10:21:18
Got it in 0.02 in C and 0.10 in Java.


kanishkajoshi:
20160530 13:55:49
after 4 months i got AC in one go 1st time :)


cena_coder:
20160526 19:53:29
TLE :(

Added by:  adrian 
Date:  20040509 
Time limit:  6s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL 6 VB.net 
Resource:  ACM Central European Programming Contest, Prague 2000 