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;
int iter = 0, iter2 = 0;
int used[1003][1003], visit[1003];
int F[1003][1003], C[1003][1003];
vector<int> adj[1003];
int n, pi[1003];
int src, snk;
bool dfs(int u) {
  visit[u] = iter2;
  if (u == snk) {
    while (u != src) {
      F[u][pi[u]] = -(++F[pi[u]][u]);
      u = pi[u];
    }
    return true;
  }
  int v;
  for (int i = 0; i < adj[u].size(); ++i) {
    v = adj[u][i];
    if (C[u][v] - F[u][v] and used[u][v] != iter and visit[v] != iter2) {
      used[u][v] = iter;
      pi[v] = u;
      if (dfs(v)) return true;
    }
  }
  return false;
}
int maxflow() {
  int flow = 0, cnt = 0;
  do {
    ++iter;
    cnt = 0;
    ++iter2;
    while (dfs(src)) {
      ++iter2;
      cnt++;
      flow++;
    }
  } while (cnt);
  return flow;
}
bool prime[20001];
bool vis[200];
int v[200];
vector<int> cmp;
vector<int> tmp[200];
void dfs2(int x) {
  vis[x] = true;
  cmp.push_back(x);
  for (int y : tmp[x]) {
    if (!vis[y]) {
      dfs2(y);
    }
  }
}
void init() {
  memset(prime, 1, sizeof prime);
  for (int i = 2; i * i < 20001; ++i) {
    if (prime[i])
      for (int j = i * i; j < 20001; j += i) prime[j] = false;
  }
}
int main() {
  ios::sync_with_stdio(false);
  init();
  int n;
  cin >> n;
  int cnt = 0;
  for (int i = 0; i < n; ++i) {
    cin >> v[i];
    cnt += v[i] & 1;
  }
  bool ok = cnt * 2 == n;
  if (ok) {
    src = n;
    snk = n + 1;
    for (int i = 0; i < n; ++i) {
      if (v[i] & 1) {
        adj[src].push_back(i);
        C[src][i] = 2;
        for (int j = 0; j < n; ++j) {
          if (prime[v[i] + v[j]]) {
            adj[i].push_back(j);
            C[i][j] = 1;
            adj[j].push_back(i);
          }
        }
      } else {
        adj[i].push_back(snk);
        C[i][snk] = 2;
      }
    }
    int mf = maxflow();
    ok &= mf == n;
    if (ok) {
      for (int i = 0; i < n; ++i) {
        if (v[i] & 1) {
          for (int u : adj[i]) {
            if (F[i][u] == 1) {
              tmp[i].push_back(u);
              tmp[u].push_back(i);
            }
          }
        }
      }
      vector<vector<int> > ans;
      for (int i = 0; i < n; ++i) {
        if (!vis[i]) {
          cmp.clear();
          dfs2(i);
          ans.push_back(cmp);
        }
      }
      cout << ans.size() << endl;
      for (vector<int>& c : ans) {
        cout << c.size();
        for (int id : c) {
          cout << " " << id + 1;
        }
        cout << endl;
      }
      return 0;
    }
  }
  cout << "Impossible" << endl;
  return 0;
}