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 T1>
void deb(T1 e) {
  cout << e << endl;
}
template <class T1, class T2>
void deb(T1 e1, T2 e2) {
  cout << e1 << " " << e2 << endl;
}
template <class T1, class T2, class T3>
void deb(T1 e1, T2 e2, T3 e3) {
  cout << e1 << " " << e2 << " " << e3 << endl;
}
template <class T1, class T2, class T3, class T4>
void deb(T1 e1, T2 e2, T3 e3, T4 e4) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << endl;
}
template <class T1, class T2, class T3, class T4, class T5>
void deb(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << " " << e5 << endl;
}
template <class T1, class T2, class T3, class T4, class T5, class T6>
void deb(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5, T6 e6) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << " " << e5 << " " << e6
       << endl;
}
int arr[210], n;
const int INF = 2000000000;
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 < 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 < G[t].size(); i++) {
      Edge *start = &G[G[t][i].to][G[t][i].index];
      int amt = INF;
      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;
  }
};
Dinic *mf = new Dinic(210);
bool prime[20010];
bool sieve[20010];
void SOE() {
  int i, j, r;
  prime[2] = 1;
  for (i = 3; i <= 20010 - 1; i += 2) {
    if (sieve[i] == false) {
      prime[i] = 1;
      if (i < (20010 - 1) / i) {
        r = (i << 1);
        for (j = (i * i); j < (20010 - 1); j += r) sieve[j] = true;
      }
    }
  }
  return;
}
void pre() {
  SOE();
  int i, j;
  for (i = 1; i <= n; i++) {
    if (arr[i] & 1) {
      mf->AddEdge(0, i, 2);
      for (j = 1; j <= n; j++)
        if (arr[j] % 2 == 0 && prime[arr[j] + arr[i]]) mf->AddEdge(i, j, 1);
    } else
      mf->AddEdge(i, n + 1, 2);
  }
}
vector<int> temp;
vector<vector<int>> ans;
vector<int> adj[210];
bool col[210];
bool okay(int a, int b) { return a >= 1 && b >= 1 && a <= n && b <= n; }
void dfs(int u) {
  int i, v;
  for (i = 0; i < adj[u].size(); i++) {
    v = adj[u][i];
    if (!col[v]) {
      temp.push_back(v);
      col[v] = 1;
      dfs(v);
    }
  }
}
void solve() {
  int i, j;
  for (i = 0; i < mf->G.size(); i++)
    for (j = 0; j < mf->G[i].size(); j++) {
      if (mf->G[i][j].flow != 0 && okay(mf->G[i][j].from, mf->G[i][j].to))
        adj[mf->G[i][j].from].push_back(mf->G[i][j].to);
    }
  for (i = 1; i <= n; i++)
    if (!col[i]) {
      temp.clear();
      col[i] = 1;
      temp.push_back(i);
      dfs(i);
      ans.push_back(temp);
    }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  int i, j;
  cin >> n;
  for (i = 1; i <= n; i++) cin >> arr[i];
  pre();
  if (mf->GetMaxFlow(0, n + 1) != n) {
    deb("Impossible");
    return 0;
  }
  solve();
  deb(ans.size());
  for (i = 0; i < ans.size(); i++) {
    cout << ans[i].size() << " ";
    for (j = 0; j < ans[i].size(); j++) cout << ans[i][j] << " ";
    cout << endl;
  }
  return 0;
}