Score : 1200 points

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.

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 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