Sequence

We call a sequence of numbers an arithmetic sequence in base $b$ if, when each number is read as a base-$b$ numeral, consecutive terms differ by a constant.

For example, $1, 1010, 2012, 10021$ is an arithmetic sequence in base $3$, and $11, 33, 55$ is an arithmetic sequence not only in base $10$ but also in base $6$.

Given a sequence of numbers, find the smallest base (at most $10$) in which the numbers form an arithmetic sequence.

If the largest digit appearing in any number is $d$, then the base must be at least $d+1$ for every digit to be valid, and it is always at least $2$.

The input consists of several test cases.

The first line of each test case contains an integer $n$ ($2 \le n \le 5$), the count of numbers in the sequence. The next line contains the $n$ numbers in strictly increasing order, separated by single spaces.

A line containing $n = 0$ terminates the input. Every number is positive, uses only the digits $0$ through $9$, and has at most $5$ digits.

For each test case, print a single line.

If such a base exists, print

Minimum base = x.

where $x$ is the smallest base $\le 10$ that yields an arithmetic sequence. Otherwise, print

No base <= 10 can be found.