#include <map>
#include <cstdio>
#include <cstring>

inline int Abs(const int x){return x>=0?x:-x;}

int n,a[205],b[205],Mat[205],Ans;
bool G[205][205],Vis[205];
std::map<int,int> M;

bool Prime(int x)
{
    if(x<2)return false;
    for(int i=2;i*i<=x;++i)
        if(x%i==0)return false;
    return true;
}

bool DFS(int x)
{
    for(int y=1;y<=n;++y)
        if(!Vis[y]&&G[x][y])
            if(Vis[y]=true,!Mat[y]||DFS(Mat[y]))
                return Mat[y]=x,true;
    return false;
}

int main()
{
    scanf("%d",&n);
    for(int i=1,x;i<=n;++i)scanf("%d",&x),M[x]^=1,M[x+1]^=1;
    for(auto i:M)if(i.second)(i.first&1?a[++*a]:b[++*b])=i.first;
    for(int i=1;i<=*a;++i)
        for(int j=1;j<=*b;++j)
            G[i][j]=Prime(Abs(a[i]-b[j]));
    for(int i=1;i<=*a;++i)memset(Vis,0,sizeof Vis),Ans+=DFS(i);
    printf("%d\n",Ans+(*a-Ans)/2*2+(*b-Ans)/2*2+(*a-Ans)%2*3);
    return 0;
}
### Prompt

Your task is to create a cpp solution to the following problem:

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.

Examples

Input

2
4 5


Output

2


Input

9
1 2 3 4 5 6 7 8 9


Output

3


Input

2
1 10000000


Output

4

### Response

```cpp
#include <map>
#include <cstdio>
#include <cstring>

inline int Abs(const int x){return x>=0?x:-x;}

int n,a[205],b[205],Mat[205],Ans;
bool G[205][205],Vis[205];
std::map<int,int> M;

bool Prime(int x)
{
    if(x<2)return false;
    for(int i=2;i*i<=x;++i)
        if(x%i==0)return false;
    return true;
}

bool DFS(int x)
{
    for(int y=1;y<=n;++y)
        if(!Vis[y]&&G[x][y])
            if(Vis[y]=true,!Mat[y]||DFS(Mat[y]))
                return Mat[y]=x,true;
    return false;
}

int main()
{
    scanf("%d",&n);
    for(int i=1,x;i<=n;++i)scanf("%d",&x),M[x]^=1,M[x+1]^=1;
    for(auto i:M)if(i.second)(i.first&1?a[++*a]:b[++*b])=i.first;
    for(int i=1;i<=*a;++i)
        for(int j=1;j<=*b;++j)
            G[i][j]=Prime(Abs(a[i]-b[j]));
    for(int i=1;i<=*a;++i)memset(Vis,0,sizeof Vis),Ans+=DFS(i);
    printf("%d\n",Ans+(*a-Ans)/2*2+(*b-Ans)/2*2+(*a-Ans)%2*3);
    return 0;
}
```