### ACSL Practice 2009

The factorial of a positive integer n, written as n!, is the product of the first n positive integers. That is,

n! = 1 × 2 × ... × n

Given a positive integer n, find the number of zeros in the decimal representation of n!. Of course, leading zeros should not be counted. (Note that decimal representation means base ten representation.)

Example 1. There are 7 zeros in the decimal representation of 20!.

20! = 1 × 2 × ... × 19 × 20 = 2432902008176640000

Example 2. There are 2 zeros in the decimal representation of 7!.

7! = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040

Example 3. There is no zero in the decimal representation of 4!.

4! = 1 × 2 × 3 × 4 = 24

### Input

The input contains a single positive integer n ≤ 100.

### Output

The number of zeros in the decimal representation of n!.

`20`

`7`

`7`

`2`

`4`

### Output

`0`

Point Value: 10
Time Limit: 2.00s
Memory Limit: 16M

Languages Allowed:
C++03, PAS, C, ASM, PHP, C#, C++11

• (0/0)
Is my code entirely too slow?

• (1/0)
It doesn't appear to me that you've run your program on the sample input.

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Clarify?

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Your program fails to produce a value for the sample inputs.

You may wish to take a closer look at your loops.

• (1/0)
Duplication error occured to this question after value change...

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No idea what caused this. Should be fixed.

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We can't submit this code in Java??

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Java natively supports bignums so it's disallowed in this problem.

• (0/0)
Alvin, you hard coded!

• (7/0)
Hard-coding doesn't negatively affect your performance in ACSL. Their Contests were based on hard-coding.

• (0/0)
i did string multiply after