Problem: Fox Ciel is participating in a party in Prime Kingdom. There are n foxes there (include Fox Ciel). The i-th fox is ai years old.

They will have dinner around some round tables. You want to distribute foxes such that:

  1. Each fox is sitting at some table. 
  2. Each table has at least 3 foxes sitting around it. 
  3. The sum of ages of any two adjacent foxes around each table should be a prime number. 



If k foxes f1, f2, ..., fk are sitting around table in clockwise order, then for 1 ≤ i ≤ k - 1: fi and fi + 1 are adjacent, and f1 and fk are also adjacent.

If it is possible to distribute the foxes in the desired manner, find out a way to do that.

Input

The first line contains single integer n (3 ≤ n ≤ 200): the number of foxes in this party. 

The second line contains n integers ai (2 ≤ ai ≤ 104).

Output

If it is impossible to do this, output "Impossible".

Otherwise, in the first line output an integer m (<image>): the number of tables.

Then output m lines, each line should start with an integer k -=– the number of foxes around that table, and then k numbers — indices of fox sitting around that table in clockwise order.

If there are several possible arrangements, output any of them.

Examples

Input

4
3 4 8 9


Output

1
4 1 2 4 3


Input

5
2 2 2 2 2


Output

Impossible


Input

12
2 3 4 5 6 7 8 9 10 11 12 13


Output

1
12 1 2 3 6 5 12 9 8 7 10 11 4


Input

24
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25


Output

3
6 1 2 3 6 5 4
10 7 8 9 12 15 14 13 16 11 10
8 17 18 23 22 19 20 21 24

Note

In example 1, they can sit around one table, their ages are: 3-8-9-4, adjacent sums are: 11, 17, 13 and 7, all those integers are primes.

In example 2, it is not possible: the sum of 2+2 = 4 is not a prime number.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int inf = (1 << 30) - 1;
const long long linf = (1ll << 62) - 1;
bool isPrime(int n) {
  if (n == 1) {
    return false;
  }
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
const int N = 300;
int n;
int a[N];
int mt[N];
vector<int> g[N];
int used[N];
vector<vector<int> > ans;
inline int kuhn(int v) {
  if (used[v]) {
    return false;
  }
  used[v] = 1;
  for (int to : g[v]) {
    if (mt[to] == -1 || kuhn(mt[to])) {
      mt[to] = v;
      return true;
    }
  }
  return false;
}
int s[N];
void check(const vector<int> &x) {
  for (int i = 0; i < ((int)(x).size()); i++) {
    assert(isPrime(a[x[i]] + a[x[(i + 1) % ((int)(x).size())]]));
  }
  assert(((int)(x).size()) >= 3);
}
int main() {
  double start = clock();
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (isPrime(a[i] + a[j])) {
        g[i].push_back(j);
      }
    }
  }
  for (int i = 0; i < n; i++) {
    s[i] = i;
  }
  while (1.0 * (clock() - start) / CLOCKS_PER_SEC < 1.9) {
    fill_n(mt, n, -1);
    for (int i = 0; i < n; i++) {
      random_shuffle((g[i]).begin(), (g[i]).end());
    }
    for (int i = 0; i < n; i++) {
      fill_n(used, n, false);
      if (!kuhn(s[i])) {
        puts("Impossible");
        return 0;
      }
    }
    int cnt = 0;
  label:;
    bool flag = true;
    for (int i = 0; i < n; i++) {
      if (mt[mt[i]] == i) {
        if (cnt++ <= 10) {
          int v = mt[i];
          mt[i] = -1;
          fill_n(used, n, false);
          if (!kuhn(v)) {
            puts("Impossible");
            return 0;
          }
          goto label;
        }
        flag = false;
        break;
      }
    }
    if (!flag) {
      random_shuffle(s, s + n);
      continue;
    }
    fill_n(used, n, false);
    for (int i = 0; i < n; i++) {
      if (!used[i]) {
        vector<int> cur;
        cur.push_back(i);
        used[i] = true;
        int I = mt[i];
        while (I != i) {
          used[I] = true;
          cur.push_back(I);
          I = mt[I];
        }
        ans.push_back(cur);
      }
    }
    break;
  }
  if (((int)(ans).size()) == 0) {
    puts("Impossible");
    return 0;
  }
  cout << ((int)(ans).size()) << endl;
  for (auto i : ans) {
    check(i);
    cout << ((int)(i).size()) << ' ';
    for (int j : i) {
      cout << j + 1 << ' ';
    }
    cout << "\n";
  }
  return 0;
}