Problem D
Digit Product
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Consider a positive integer $x$. Multiply its nonzero digits and you get another integer $y$. Repeating this process, you eventually arrive at a single digit between $1$ and $9$. Write a program that reads $x$ and outputs the resulting digit.
Input
An integer $x$ with $10 \leq x \leq 1\, 000$.
Output
Print a digit between $1$ and $9$, the result of repeatedly multiplying the nonzero digits of $x$ as described above.
Explanation of Sample Inputs
In Sample Input $1$, we have $x = 808$. Multiplying $8$ and $8$, we arrive at $64$. Then we get $6 \cdot 4 = 24$, and finally $2 \cdot 4 = 8$, which is the sample output.
In Sample Input $2$, there is only a single nonzero digit, $2$. The product of all digits in a set containing only a single element is the digit itself. Thus the answer is $2$.
| Sample Input 1 | Sample Output 1 |
|---|---|
808 |
8 |
| Sample Input 2 | Sample Output 2 |
|---|---|
20 |
2 |
