#include <bits/stdc++.h>
using namespace std;
const int N = 2e6 + 7;
int vis[N];
void Getprime() {
  int sq = sqrt(N);
  for (int i = 2; i < sq; i++) {
    for (int j = i * i; j < N; j += i) vis[j] = 1;
  }
}
int in[1007];
int main() {
  Getprime();
  int n, num_1 = 0, ans = 0, l = 0, r = 0;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", in + i);
    if (in[i] == 1) num_1++;
  }
  sort(in, in + n);
  int p = upper_bound(in, in + n, 1) - in;
  for (int i = 0; i < n; i++) {
    for (int j = max(i + 1, p); j < n; j++)
      if (vis[in[i] + in[j]] == 0) {
        l = in[i], r = in[j];
        i = j = n;
      }
  }
  if (l == 1) {
    printf("%d\n", num_1 + 1);
    for (int i = 1; i < num_1 + 1; i++) printf("1 ");
    printf("%d", r);
  } else if (num_1 > 1) {
    printf("%d\n", num_1);
    while (num_1--) printf("1 ");
  } else if (l) {
    printf("2\n%d %d", l, r);
  } else {
    printf("1\n%d", in[0]);
  }
}

### Prompt

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

A tuple of positive integers {x1, x2, ..., xk} is called simple if for all pairs of positive integers (i, j) (1 ≤ i < j ≤ k), xi + xj is a prime.

You are given an array a with n positive integers a1, a2, ..., an (not necessary distinct). You want to find a simple subset of the array a with the maximum size.

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Let's define a subset of the array a as a tuple that can be obtained from a by removing some (possibly all) elements of it.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — the number of integers in the array a.

The second line contains n integers ai (1 ≤ ai ≤ 106) — the elements of the array a.

Output

On the first line print integer m — the maximum possible size of simple subset of a.

On the second line print m integers bl — the elements of the simple subset of the array a with the maximum size.

If there is more than one solution you can print any of them. You can print the elements of the subset in any order.

Examples

Input

2
2 3


Output

2
3 2


Input

2
2 2


Output

1
2


Input

3
2 1 1


Output

3
1 1 2


Input

2
83 14


Output

2
14 83

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 2e6 + 7;
int vis[N];
void Getprime() {
  int sq = sqrt(N);
  for (int i = 2; i < sq; i++) {
    for (int j = i * i; j < N; j += i) vis[j] = 1;
  }
}
int in[1007];
int main() {
  Getprime();
  int n, num_1 = 0, ans = 0, l = 0, r = 0;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", in + i);
    if (in[i] == 1) num_1++;
  }
  sort(in, in + n);
  int p = upper_bound(in, in + n, 1) - in;
  for (int i = 0; i < n; i++) {
    for (int j = max(i + 1, p); j < n; j++)
      if (vis[in[i] + in[j]] == 0) {
        l = in[i], r = in[j];
        i = j = n;
      }
  }
  if (l == 1) {
    printf("%d\n", num_1 + 1);
    for (int i = 1; i < num_1 + 1; i++) printf("1 ");
    printf("%d", r);
  } else if (num_1 > 1) {
    printf("%d\n", num_1);
    while (num_1--) printf("1 ");
  } else if (l) {
    printf("2\n%d %d", l, r);
  } else {
    printf("1\n%d", in[0]);
  }
}

```