Description

There are $n$ distinct integers. Now there are $m$ integers that belong to the set $G$.

Aw Dundun defines this set with the following rules:

• If $x \in G$, then $x + a \in G$.
• If $x + a$ is not among the $n$ integers, then do nothing.
• If for a set $G$ there are no elements that need to be added, then it is complete.

If the set is complete, output Great Set!. Otherwise, output at least how many more ingredients must be added according to the rules to make it complete.

Input Format

The first line is an integer $n$, meaning there are $n$ integers in total.

The next line contains $n$ integers $A_i$ separated by spaces, all distinct.

The next line is a positive integer $m$, meaning there are $m$ integers in the set $G$, and all of them are among the $n$ integers.

The next line contains $m$ integers separated by spaces.

The last line is a positive integer $a$.

Output Format

If this set is already complete, output Great Set!.

Otherwise, output the number of integers needed to make this set complete.

5
1 2 3 4 5
3
1 3 5
2

Great Set!

15
13 2 10 3 1 12 8 4 5 7 9 6 15 14 11 
7
13 2 1 12 8 3 10 
2

8

50
13 2 10 50 1 28 37 32 30 46 19 47 33 41 24 34 27 42 49 18 9 48 23 35 31 8 7 12 6 5 3 22 43 36 11 40 26 4 44 17 39 38 15 14 25 16 29 20 21 45 
10
50 46 30 32 10 2 28 37 1 13 
3

31

Hint

Sample Explanation

Sample 1 Explanation

This set contains $1, 3, 5$. Here, $1 + 2 = 3$, $3 + 2 = 5$, and $5 + 2 = 7$ does not exist, so this set is complete.

Sample 2 Explanation

All remaining integers belong to this set.

Constraints

• $1 \le m < n \le 6 \times 10^4$.
• $1 \le A_i \le n$.
• $0 \le a \le 10^4$.

Bundled Testcases

$\rm P.S.$ The time limit for this problem has been set to $\bf 15$ times that of $\rm std$. Some test points are included in the attachment.

Translated by ChatGPT 5