Problem Statement

\(N\) distinct digits from '\(0\)' to '\(9\)' are given.

Next, from the range between \(1\) and \(5000000\), inclusive, choose a range from \(K\) to \(L\), inclusive.
Extract all the primes, and only the primes, from the range from \(K\) to \(L\).
Examine the digits used across all of these primes.
For example, if the range from \(10\) to \(20\) is chosen as the range from \(K\) to \(L\),
the primes are the \(4\) numbers "\(11\)", "\(13\)", "\(17\)", and "\(19\)".
The digits used are the \(4\) digits '\(1\)', '\(3\)', '\(7\)', and '\(9\)'.
We want these used digits to be equal to the digits given at the beginning.
(All of them must be used.)
Find the maximum value of the difference \(L-K\) between \(K\) and \(L\) in this situation.
If no such case exists, the answer is \(-1\).

The following are invalid examples.
Suppose the given digits are \([3,5,7]\).
The primes in the range from \(4\) to \(7\) are \(5,7\), which do not include \(3\), so this is an invalid range.
The primes in the range from \(2\) to \(10\) are \(2,3,5,7\), which include an extra \(2\), so this is an invalid range.

In this case, ranges such as "from \(3\) to \(7\)" and "from \(3\) to \(10\)" are valid.

Input

\(N\)
\(A_1\ \dots\ A_i\ \dots\ A_N\)

Line \(1\) contains the number of given digits \(N\ (1 \leq N \leq 10)\).
Line \(2\) contains the \(N\) given digits \(A_i\ (0 \leq A_i \leq 9)\), separated by single-byte spaces.
If $i \neq j$, then $A_i \neq A_j$.

Output

Find the maximum value of the difference \(L-K\) between \(K\) and \(L\).
If nothing satisfies the conditions, the answer is \(-1\).
Print a newline at the end.

Sample

1
5

2

5
1 2 3 4 5

158

2
0 3

-1

10
0 1 2 3 4 5 6 7 8 9

4999999

2
1 3

94