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;
vector<pair<int, int> > odd;
vector<pair<int, int> > even;
vector<int> v[202];
int cap[202][202], prime[20000 + 1], viz[202], p[202], q[202];
void ciur(int n) {
  int i, j;
  for (i = 2; i <= n; i = i + 1)
    if (prime[i] == 0) {
      for (j = i + i; j <= n; j = j + i) prime[j] = 1;
    }
}
int is_prime(int x) { return prime[x] == 0; }
int bfs(int source, int dest) {
  int st, dr, nod;
  memset(viz, 0, sizeof(viz));
  memset(p, 0, sizeof(p));
  st = dr = 1;
  q[st] = source;
  viz[source] = 1;
  while (st <= dr) {
    nod = q[st];
    st++;
    for (vector<int>::iterator it = v[nod].begin(); it != v[nod].end(); it++)
      if (viz[*it] == 0 && cap[nod][*it] > 0) {
        viz[*it] = 1;
        q[++dr] = *it;
        p[*it] = nod;
        if (*it == dest) break;
      }
    if (p[dest]) break;
  }
  if (p[dest] == 0) return 0;
  int flow = (1 << 30);
  for (nod = dest; nod != 0; nod = p[nod]) flow = min(flow, cap[p[nod]][nod]);
  return flow;
}
int max_flow(int n) {
  int flow = 0, current_flow;
  while ((current_flow = bfs(0, n + 1))) {
    for (int nod = n + 1; nod != 0; nod = p[nod]) {
      cap[p[nod]][nod] -= current_flow;
      cap[nod][p[nod]] += current_flow;
    }
    flow += current_flow;
  }
  return flow;
}
void build_table(int nod, vector<int>& table) {
  if (viz[nod] == 1) return;
  viz[nod] = 1;
  table.push_back(nod);
  for (vector<pair<int, int> >::iterator it = odd.begin(); it != odd.end();
       it++)
    if (cap[it->second][nod] == 1) {
      cap[it->second][nod] = 0;
      nod = it->second;
      break;
    }
  table.push_back(nod);
  for (vector<pair<int, int> >::iterator it = even.begin(); it != even.end();
       it++)
    if (cap[nod][it->second] == 1) {
      cap[nod][it->second] = 0;
      nod = it->second;
      break;
    }
  build_table(nod, table);
}
int main() {
  int n, i, x;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> x;
    if (x & 1)
      odd.push_back(make_pair(x, i));
    else
      even.push_back(make_pair(x, i));
  }
  if (odd.size() != even.size()) {
    cout << "Impossible\n";
    return 0;
  }
  for (vector<pair<int, int> >::iterator it = even.begin(); it != even.end();
       it++) {
    v[0].push_back(it->second);
    v[it->second].push_back(0);
    cap[0][it->second] = 2;
  }
  for (vector<pair<int, int> >::iterator it = odd.begin(); it != odd.end();
       it++) {
    v[it->second].push_back(n + 1);
    v[n + 1].push_back(it->second);
    cap[it->second][n + 1] = 2;
  }
  ciur(20000);
  for (vector<pair<int, int> >::iterator st = even.begin(); st != even.end();
       st++) {
    for (vector<pair<int, int> >::iterator dr = odd.begin(); dr != odd.end();
         dr++) {
      if (is_prime(st->first + dr->first)) {
        v[st->second].push_back(dr->second);
        v[dr->second].push_back(st->second);
        cap[st->second][dr->second] = 1;
      }
    }
  }
  int flow = max_flow(n);
  if (flow != n) {
    cout << "Impossible\n";
    return 0;
  }
  int num_nodes = 0;
  memset(viz, 0, sizeof(viz));
  vector<vector<int> > sol;
  while (num_nodes < n) {
    for (vector<pair<int, int> >::iterator it = even.begin(); it != even.end();
         it++)
      if (viz[it->second] == 0) {
        vector<int> table;
        build_table(it->second, table);
        sol.push_back(table);
        num_nodes += table.size();
      }
  }
  cout << sol.size() << '\n';
  int nr = sol.size();
  for (i = 0; i < nr; i++) {
    cout << sol[i].size() << " ";
    for (vector<int>::iterator it = sol[i].begin(); it != sol[i].end(); it++)
      cout << *it << " ";
    cout << '\n';
  }
  return 0;
}