Problem C
The Magical 3
Even more magically, almost all integers can be represented as a number that ends in 3 in some numeric base, sometimes in more than one way. Consider the number 11, which is represented as 13 in base 8 and 23 in base 4. For this problem, you will find the smallest base for a given number so that the number’s representation in that base ends in 3.
Input
Each line of the input contains one nonnegative integer $n$. The value $n = 0$ represents the end of the input and should not be processed. All input integers are less than $2^{31}$. There are no more than $1\, 000$ nonzero values of $n$.
Output
For each nonzero value of $n$ in the input, print on a single line the smallest base for which the number has a representation that ends in 3. If there is no such base, print instead “No such base”.
| Sample Input 1 | Sample Output 1 |
|---|---|
11 123 104 2 3 0 |
4 4 101 No such base 4 |
