There are infinitely many cards, numbered 1, 2, 3, ...
Initially, Cards x_1, x_2, ..., x_N are face up, and the others are face down.
Snuke can perform the following operation repeatedly:
- Select a prime p greater than or equal to 3. Then, select p consecutive cards and flip all of them.
Snuke's objective is to have all the cards face down.
Find the minimum number of operations required to achieve the objective.

-----Constraints-----
- 1 ≤ N ≤ 100
- 1 ≤ x_1 < x_2 < ... < x_N ≤ 10^7

-----Input-----
Input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N

-----Output-----
Print the minimum number of operations required to achieve the objective.

-----Sample Input-----
2
4 5

-----Sample Output-----
2

Below is one way to achieve the objective in two operations:
- Select p = 5 and flip Cards 1, 2, 3, 4 and 5.
- Select p = 3 and flip Cards 1, 2 and 3.

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