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he 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 N1<N2, then Z(N1) <= Z(N2). 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.InputThere 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.OutputFor every number N, output a single line containing the single non-negative integer Z(N).ExampleSample Input:63601001024234568735373Sample Output:0142425358612183837

Question

he 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 N1<N2, then Z(N1) <= Z(N2). 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.InputThere 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.OutputFor every number N, output a single line containing the single non-negative integer Z(N).ExampleSample Input:63601001024234568735373Sample Output:0142425358612183837

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Solution

This problem is asking for a program that calculates the number of trailing zeros in the factorial of a number. The factorial of a number N is the product of all positive integers less than or equal to N.

Here's a step-by-step guide on how to solve this problem:

  1. Understand the problem: The problem is asking for the number of trailing zeros in the factorial of a number. A trailing zero is formed by a product of 2 and 5. Since the number of 2s would be abundant, we need to count the number of 5s in the factors of the number.

  2. Create a function to calculate the number of trailing zeros: This function will take an integer N as input and return the number of trailing zeros in N!.

  3. In this function, initialize a variable count to 0. This variable will keep track of the number of trailing zeros.

  4. Create a while loop where N is greater than 0. Inside this loop, divide N by 5 and add the result to count. This is because a trailing zero is added for every power of 5 that N is divisible by.

  5. After the loop, return count. This is the number of trailing zeros in N!.

  6. For each number in the input, call this function and print the result.

Here's a Python solution for the problem:

def find_trailing_zeros(n):
    count = 0
    i = 5
    while (n / i >= 1):
        count += int(n / i)
        i *= 5
    return int(count)

t = int(input())
for _ in range(t):

This problem has been solved

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