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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.
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 231. There are no more than 1 000 nonzero values of n.
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”.
11 123 104 2 3 0
4 4 101 No such base 4