#include <bits/stdc++.h>
using namespace std;
int n, a[1010];
bool is_prime(int num) {
  for (int i = 2; i * i <= num; i++)
    if (num % i == 0) return false;
  return true;
}
int main() {
  scanf("%d", &n);
  int cnt = 0;
  int flag = -1;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    if (a[i] == 1) cnt++;
    if (a[i] != 1 && is_prime(a[i] + 1)) flag = a[i];
  }
  if (cnt && flag != -1 && cnt + 1 > 2) {
    printf("%d\n", cnt + 1);
    while (cnt--) printf("1 ");
    printf("%d\n", flag);
    return 0;
  } else if (cnt >= 2) {
    printf("%d\n", cnt);
    while (cnt--) printf("1 ");
    printf("\n");
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      if (is_prime(a[i] + a[j])) {
        printf("2\n");
        printf("%d %d\n", a[i], a[j]);
        return 0;
      }
    }
  }
  printf("1\n");
  printf("%d\n", a[1]);
  return 0;
}

### Prompt

Generate 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;
int n, a[1010];
bool is_prime(int num) {
  for (int i = 2; i * i <= num; i++)
    if (num % i == 0) return false;
  return true;
}
int main() {
  scanf("%d", &n);
  int cnt = 0;
  int flag = -1;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    if (a[i] == 1) cnt++;
    if (a[i] != 1 && is_prime(a[i] + 1)) flag = a[i];
  }
  if (cnt && flag != -1 && cnt + 1 > 2) {
    printf("%d\n", cnt + 1);
    while (cnt--) printf("1 ");
    printf("%d\n", flag);
    return 0;
  } else if (cnt >= 2) {
    printf("%d\n", cnt);
    while (cnt--) printf("1 ");
    printf("\n");
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      if (is_prime(a[i] + a[j])) {
        printf("2\n");
        printf("%d %d\n", a[i], a[j]);
        return 0;
      }
    }
  }
  printf("1\n");
  printf("%d\n", a[1]);
  return 0;
}

```