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

• $1 \leq N \leq 100$
• $1 \leq x_1 < x_2 < ... < x_N \leq 10^7$

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.

2
4 5

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 $3$.

9
1 2 3 4 5 6 7 8 9

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 $9$.

2
1 10000000

4