Problem:
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

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

int n,x,a[222],b[222],m,ans=1e8,an,c[2];
map<int,int>mp;
struct E{
	int u,v;
}e[44444];

bool pri(int x){
	if (x%2==0||x==1) return 0;
	for (int i=3;i*i<=x;++i) if (x%i==0)
		return 0;
	return 1;
}

int main(){
	for (cin>>n;n--;)
		cin>>x, mp[x]^=1, mp[x+1]^=1;
	n=0;
	for (auto o:mp) if (o.second)
		a[++n]=o.first;
	for (int i=1;i<n;++i)
		for (int j=i+1;j<=n;++j) if (pri(abs(a[i]-a[j])))
			e[++m]=(E){i,j};
	for (int t=10000;t--;){
		random_shuffle(e+1,e+m+1);
		memset(b,0,sizeof b); an=0;
		for (int i=1;i<=m;++i){
			if (!b[e[i].u]&&!b[e[i].v])
				b[e[i].u]=b[e[i].v]=1, ++an;
		}
		c[0]=c[1]=0;
		for (int i=1;i<=n;++i) if (!b[i])
			++c[a[i]&1];
		an+=(c[0]/2+c[1]/2)*2+c[0]%2*3;
		ans=min(ans,an);
	}
	cout<<ans;
}