Competitions

# The Magical 3

There's no doubt about it, three is a magical number. Two's company, but three's a crowd, no one ever talks about 2 blind mice, and there are three members in an ACM ICPC team.

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 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 231. There are no more than 1000 nonzero values of n.

#### Output

For each nonzero value of n 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”.

Time limit 1 second
Memory limit 122.17 MiB
Input example #1
11
123
104
2
3
0

Output example #1
4
4
101
No such base
4

Source 2015 ACM North America - Rocky Mountain, Problem H