10813: ABC148 - E - Double Factorial
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Description
For an integer $n$ not less than $0$, let us define $f(n)$ as follows:
- $f(n) = 1$ (if $n < 2$)
- $f(n) = n f(n-2)$ (if $n \geq 2$)
Given is an integer $N$. Find the number of trailing zeros in the decimal notation of $f(N)$.
- $f(n) = 1$ (if $n < 2$)
- $f(n) = n f(n-2)$ (if $n \geq 2$)
Given is an integer $N$. Find the number of trailing zeros in the decimal notation of $f(N)$.
Input
Input is given from Standard Input in the following format:
```
$N$
```
```
$N$
```
Output
Print the number of trailing zeros in the decimal notation of $f(N)$.
Constraints
$0 \leq N \leq 10^{18}$
Sample 1 Input
12
Sample 1 Output
1
$f(12) = 12 × 10 × 8 × 6 × 4 × 2 = 46080$, which has one trailing zero.
Sample 2 Input
5
Sample 2 Output
0
$f(5) = 5 × 3 × 1 = 15$, which has no trailing zeros.
Sample 3 Input
1000000000000000000
Sample 3 Output
124999999999999995