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 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;
  }
};
std::vector<int> adj[1000], ansarr[1000];
int mark[10000], arr[10000], prime[110000];
void seive() {
  int i, j;
  for (i = 2; i < 21000; i++) prime[i] = 1;
  for (i = 2; i < 21000; i++) {
    if (prime[i] == 1) {
      j = i + i;
      while (j < 21000) {
        prime[j] = 0;
        j += i;
      }
    }
  }
}
Dinic graph(10000);
void make_graph(int n) {
  for (int i = 0; i < n; i++) {
    if (arr[i] & 1)
      graph.AddEdge(0, i + 1, 2);
    else
      graph.AddEdge(i + 1, n + 1, 2);
    for (int j = 0; j < n; j++) {
      if (prime[arr[i] + arr[j]] && (arr[i] & 1))
        graph.AddEdge(i + 1, j + 1, 1);
    }
  }
}
int main() {
  int n, i, j, ans, indexx;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &arr[i]);
  seive();
  make_graph(n);
  ans = graph.GetMaxFlow(0, n + 1);
  if (ans != n)
    printf("Impossible\n");
  else {
    for (i = 0; i < graph.G.size(); i++) {
      for (j = 0; j < graph.G[i].size(); j++) {
        if (abs(graph.G[i][j].flow) == 1) {
          adj[i].push_back(graph.G[i][j].to);
        }
      }
    }
    indexx = -1;
    for (i = 1; i <= n; i++) {
      if (mark[i] == 0) {
        mark[i] = 1;
        j = i;
        ansarr[++indexx].push_back(j);
        while (!(mark[adj[j][0]] && mark[adj[j][1]])) {
          if (mark[adj[j][0]] == 0)
            j = adj[j][0];
          else
            j = adj[j][1];
          mark[j] = 1;
          ansarr[indexx].push_back(j);
        }
      }
    }
    printf("%d\n", indexx + 1);
    for (i = 0; i <= indexx; i++) {
      printf("%d ", (int)ansarr[i].size());
      for (j = 0; j < ansarr[i].size(); j++) printf("%d ", ansarr[i][j]);
      printf("\n");
    }
  }
}