#### Statement

As you might already know, Ada the Ladybug is a farmer. She grows many vegetables and trees and she wants to distinguish between them. For this purpose she bought a funny signs, which contains a few digits. The digits on the sign could be arbitrarily permuted (yet not added/removed). Ada likes prime numbers so she want the signs to be prime (and obviously distinct). Can you find the number of signs with prime number which could be obtained?

**NOTE**: Number can't have leading zero!

#### Input:

The first line of input will contain 1 ≤ *T* ≤ 10000, the number of test-cases.

The next *T* lines will contain 1 ≤ *D* ≤ 9, the number of digits on sign, followed by *D* digits 0 ≤ *d _{i}* ≤ 9.

#### Output:

For each test-case, output the number of distinct primes which could be generated on given sign.

#### Example input:

5 1 9 3 1 2 3 5 1 2 0 8 9 7 1 0 6 5 7 8 2 5 1 2 7 3 1

#### Example output:

0 0 11 283 15

#### Time and memory limit:

- 4 seconds
- 64MB

**Problem source:**
SPOJ