Problem Statement

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.

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.

Constraints

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

Sample Input 1

2
4 5

Sample Output 1

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.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

3

Below is one way to achieve the objective in three operations:

• Select p = 3 and flip Cards 1, 2 and 3.
• Select p = 3 and flip Cards 4, 5 and 6.
• Select p = 3 and flip Cards 7, 8 and 9.

Sample Input 3

2
1 10000000

Sample Output 3

4

见题面 Input 部分

见题面 Output 部分