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 oo = 1 << 29;
const double EPS = 1e-9;
const int MAXN = (int)1e5 + 10;
struct Edge {
  int from, to, cap, flow, index;
  Edge(int from, int to, int cap, int flow, int index)
      : from(from), to(to), cap(cap), flow(flow), index(index) {}
};
struct Dinic {
  int N;
  vector<vector<Edge> > G;
  vector<Edge *> dad;
  vector<int> Q;
  Dinic(int N) : N(N), G(N), dad(N), Q(N) {}
  void AddEdge(int from, int to, int cap) {
    G[from].push_back(Edge(from, to, cap, 0, G[to].size()));
    if (from == to) G[from].back().index++;
    G[to].push_back(Edge(to, from, 0, 0, G[from].size() - 1));
  }
  long long BlockingFlow(int s, int t) {
    fill(dad.begin(), dad.end(), (Edge *)NULL);
    dad[s] = &G[0][0] - 1;
    int head = 0, tail = 0;
    Q[tail++] = s;
    while (head < tail) {
      int x = Q[head++];
      for (int i = 0; i < (int)G[x].size(); ++i) {
        Edge &e = G[x][i];
        if (!dad[e.to] && e.cap - e.flow > 0) {
          dad[e.to] = &G[x][i];
          Q[tail++] = e.to;
        }
      }
    }
    if (!dad[t]) return 0;
    long long totflow = 0;
    for (int i = 0; i < (int)G[t].size(); ++i) {
      Edge *start = &G[G[t][i].to][G[t][i].index];
      int amt = oo;
      for (Edge *e = start; amt && e != dad[s]; e = dad[e->from]) {
        if (!e) {
          amt = 0;
          break;
        }
        amt = min(amt, e->cap - e->flow);
      }
      if (amt == 0) continue;
      for (Edge *e = start; amt && e != dad[s]; e = dad[e->from]) {
        e->flow += amt;
        G[e->to][e->index].flow -= amt;
      }
      totflow += amt;
    }
    return totflow;
  }
  long long GetMaxFlow(int s, int t) {
    long long totflow = 0;
    while (long long flow = BlockingFlow(s, t)) totflow += flow;
    return totflow;
  }
};
bool isPrime(int v) {
  for (int i = 2; i * i <= v; ++i)
    if (v % i == 0) return false;
  return true;
}
bool mk[210];
bool odd[210];
void dfs(int v, vector<int> &cur, Dinic &flow) {
  mk[v] = true;
  cur.push_back(v);
  for (int i = 0; i < (int)((flow.G[v]).size()); ++i) {
    Edge &nx = flow.G[v][i];
    if (odd[v]) {
      if (nx.to > 1 && !mk[nx.to] && nx.flow == nx.cap) dfs(nx.to, cur, flow);
    } else {
      if (nx.to > 1 && !mk[nx.to] &&
          flow.G[nx.to][nx.index].flow == flow.G[nx.to][nx.index].cap)
        dfs(nx.to, cur, flow);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  Dinic flow(n + 2);
  vector<int> V(n);
  for (int i = 0; i < n; ++i) {
    cin >> V[i];
    odd[i + 2] = V[i] % 2 == 1;
    if (V[i] & 1)
      flow.AddEdge(0, i + 2, 2);
    else
      flow.AddEdge(i + 2, 1, 2);
    for (int j = 0; j < i; ++j)
      if (isPrime(V[i] + V[j])) {
        if (V[i] & 1)
          flow.AddEdge(i + 2, j + 2, 1);
        else
          flow.AddEdge(j + 2, i + 2, 1);
      }
  }
  if (flow.GetMaxFlow(0, 1) != n) {
    cout << "Impossible" << endl;
  } else {
    vector<vector<int> > ans;
    for (int i = 2; i < n + 2; ++i) {
      if (mk[i]) continue;
      vector<int> cur;
      dfs(i, cur, flow);
      ans.push_back(cur);
    }
    cout << (int)((ans).size()) << endl;
    for (int i = 0; i < (int)((ans).size()); ++i) {
      vector<int> &cur = ans[i];
      cout << (int)((cur).size());
      for (int j = 0; j < (int)((cur).size()); ++j) cout << " " << cur[j] - 1;
      cout << endl;
    }
  }
  return 0;
}