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;
template <class T, class U>
void ckmin(T &a, U b) {
  if (b < a) a = b;
}
template <class T, class U>
void ckmax(T &a, U b) {
  if (b > a) a = b;
}
int N;
int arr[213];
bitset<213> edge[213];
int sp[213 * 213];
vector<int> primes;
int match[213];
int ans[213];
bitset<213> seen;
vector<vector<int> > cyc;
bool dfs(int u) {
  if (seen[u]) return false;
  seen[u] = true;
  for (auto v = (0); v < (N); v++) {
    if (!edge[u][v]) continue;
    if (match[v] == -1 || dfs(match[v])) {
      match[u] = v;
      match[v] = u;
      return true;
    }
  }
  return false;
}
int matching() {
  int res = 0;
  for (auto i = (0); i < (N); i++) match[i] = -1;
  for (auto i = (0); i < (N); i++) {
    if (arr[i] & 1) continue;
    seen.reset();
    if (dfs(i)) {
      res++;
    }
  }
  return res;
}
void fail() {
  cout << "Impossible\n";
  exit(0);
}
int32_t main() {
  for (auto i = (2); i < (213 * 213); i++) {
    if (sp[i] == 0) {
      sp[i] = i;
      primes.push_back(i);
    }
    for (int p : primes) {
      if (p > sp[i] || p * i >= 213 * 213) break;
      sp[p * i] = p;
    }
  }
  cin >> N;
  if (N & 1) fail();
  for (auto i = (0); i < (N); i++) {
    cin >> arr[i];
  }
  for (auto i = (0); i < (N); i++) {
    for (auto j = (0); j < (N); j++) {
      if (i == j) continue;
      if (sp[arr[i] + arr[j]] == arr[i] + arr[j]) edge[i][j] = true;
    }
  }
  int m = matching();
  if (m != N / 2) fail();
  for (auto i = (0); i < (N); i++) {
    if (arr[i] & 1) {
      ans[i] = match[i];
    }
  }
  for (auto i = (0); i < (N); i++) {
    edge[i][match[i]] = false;
  }
  m = matching();
  if (m != N / 2) fail();
  for (auto i = (0); i < (N); i++) {
    if (!(arr[i] & 1)) {
      ans[i] = match[i];
    }
  }
  seen.reset();
  for (auto i = (0); i < (N); i++) {
    if (seen[i]) continue;
    vector<int> cur;
    int u = i;
    do {
      seen[u] = true;
      cur.push_back(u);
      u = ans[u];
    } while (u != i);
    cyc.push_back(cur);
  }
  cout << ((int)(cyc).size()) << '\n';
  for (auto i = (0); i < (((int)(cyc).size())); i++) {
    cout << ((int)(cyc[i]).size());
    for (int x : cyc[i]) {
      cout << ' ' << x + 1;
    }
    cout << '\n';
  }
  return 0;
}