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 a[205];
bool vis[205];
vector<int> g[205];
vector<int> cycle;
vector<vector<int>> ans;
struct Edge {
  int u, v;
  long long cap, flow;
  Edge() {}
  Edge(int u, int v, long long cap) : u(u), v(v), cap(cap), flow(0) {}
};
struct Dinic {
  int N;
  vector<Edge> E;
  vector<vector<int>> g;
  vector<int> d, pt;
  Dinic(int N) : N(N), E(0), g(N), d(N), pt(N) {}
  void AddEdge(int u, int v, long long cap) {
    if (u != v) {
      E.emplace_back(Edge(u, v, cap));
      g[u].emplace_back(E.size() - 1);
      E.emplace_back(Edge(v, u, 0));
      g[v].emplace_back(E.size() - 1);
    }
  }
  bool BFS(int S, int T) {
    queue<int> q({S});
    fill(d.begin(), d.end(), N + 1);
    d[S] = 0;
    while (!q.empty()) {
      int u = q.front();
      q.pop();
      if (u == T) break;
      for (int k : g[u]) {
        Edge &e = E[k];
        if (e.flow < e.cap && d[e.v] > d[e.u] + 1) {
          d[e.v] = d[e.u] + 1;
          q.emplace(e.v);
        }
      }
    }
    return d[T] != N + 1;
  }
  long long DFS(int u, int T, long long flow = -1) {
    if (u == T || flow == 0) return flow;
    for (int &i = pt[u]; i < g[u].size(); ++i) {
      Edge &e = E[g[u][i]];
      Edge &oe = E[g[u][i] ^ 1];
      if (d[e.v] == d[e.u] + 1) {
        long long amt = e.cap - e.flow;
        if (flow != -1 && amt > flow) amt = flow;
        if (long long pushed = DFS(e.v, T, amt)) {
          e.flow += pushed;
          oe.flow -= pushed;
          return pushed;
        }
      }
    }
    return 0;
  }
  long long MaxFlow(int S, int T) {
    long long total = 0;
    while (BFS(S, T)) {
      fill(pt.begin(), pt.end(), 0);
      while (long long flow = DFS(S, T)) total += flow;
    }
    return total;
  }
};
const int M = 2e4;
bool isPrime[M + 5];
int factor[M + 5];
void getPrime() {
  for (int i = 0; i <= M; i++) isPrime[i] = 1;
  isPrime[0] = isPrime[1] = 0;
  for (int i = 2; i * i <= M; i++) {
    if (isPrime[i]) {
      for (int j = i * i; j <= M; j += i) {
        isPrime[j] = 0;
        if (factor[j] == 0) factor[j] = i;
      }
    }
  }
  for (int i = 2; i <= M; i++)
    if (factor[i] == 0) factor[i] = i;
}
void dfs(int u) {
  vis[u] = 1;
  cycle.push_back(u);
  for (int i = 0; i < g[u].size(); i++) {
    int v = g[u][i];
    if (vis[v]) continue;
    dfs(v);
  }
}
vector<int> odd, even;
int main() {
  getPrime();
  int n;
  scanf("%d", &n);
  Dinic dinic(n + 2);
  int source = 0, sink = n + 1;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    if (a[i] % 2 == 1) {
      odd.push_back(i);
      dinic.AddEdge(source, i, 2);
    } else {
      even.push_back(i);
      dinic.AddEdge(i, sink, 2);
    }
  }
  for (int i = 0; i < odd.size(); i++) {
    for (int j = 0; j < even.size(); j++) {
      if (isPrime[a[odd[i]] + a[even[j]]]) {
        dinic.AddEdge(odd[i], even[j], 1);
      }
    }
  }
  int flow = dinic.MaxFlow(source, sink);
  if (odd.size() != even.size() || flow != 2 * even.size())
    printf("Impossible\n");
  else {
    for (int i = 0; i < odd.size(); i++) {
      int u = odd[i];
      for (int j = 0; j < dinic.g[u].size(); j++) {
        int idx = dinic.g[u][j];
        if (dinic.E[idx].flow == 1) {
          g[dinic.E[idx].u].push_back(dinic.E[idx].v);
          g[dinic.E[idx].v].push_back(dinic.E[idx].u);
        }
      }
    }
    for (int i = 0; i < odd.size(); i++) {
      int u = odd[i];
      if (vis[u]) continue;
      cycle.clear();
      dfs(u);
      ans.push_back(cycle);
    }
    printf("%d\n", ans.size());
    for (int i = 0; i < ans.size(); i++) {
      printf("%d ", ans[i].size());
      for (int j = 0; j < ans[i].size(); j++) printf("%d ", ans[i][j]);
      printf("\n");
    }
  }
}