Score : $300$ points

Problem Statement

Given are $N$ integers between $2$ and $50$ (inclusive): $X_1, X_2, \cdots, X_N$. Find the minimum positive integer $Y$ that satisfies the following for every $i = 1, 2, \cdots, N$:

• $X_i$ and $Y$ are not coprime.

Constraints

• $1 \leq N \leq 49$
• $2 \leq X_i \leq 50$
• $X_i \neq X_j (i \neq j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$X_1$ $X_2$ $\ldots$ $X_N$

Output

Print the minimum positive integer that satisfies the condition.

2
4 3

6

Being not coprime with $4$ requires being even, and being not coprime with $3$ requires being a multiple of $3$.

1
47

47

7
3 4 6 7 8 9 10

42