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Description

There are n positive integers $a[i]$, and let their product be p. You can multiply p by a positive integer q, so that $p*q$ is exactly the factorial of the positive integer m, and find the minimum value of m.

Input format

Two lines in total. The first line contains a positive integer n. The second line contains n positive integers $a[i]$.

Output format

There is one positive integer m in a row.

Example

1
6

3

Data scale and agreement

For 10% of the data, $n ≤ 10$

For 30% of the data, $n ≤ 1000$

For 100% of the data, $n ≤ 100000, a [i] ≤ 100000$

Time limit: $1s$

Space limit: 256MB