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 N = 500;
struct Dinic {
  int nodes, src, dst;
  vector<int> dist, q, work;
  struct edge {
    int to, rev;
    long long f, cap;
  };
  vector<vector<edge>> g;
  Dinic(int x) : nodes(x), g(x), dist(x), q(x), work(x) {}
  void add_edge(int s, int t, long long cap) {
    g[s].push_back((edge){t, ((int)g[t].size()), 0, cap});
    g[t].push_back((edge){s, ((int)g[s].size()) - 1, 0, 0});
  }
  bool dinic_bfs() {
    fill(dist.begin(), dist.end(), -1);
    dist[src] = 0;
    int qt = 0;
    q[qt++] = src;
    for (int qh = 0; qh < qt; qh++) {
      int u = q[qh];
      for (int i = 0; i < ((int)g[u].size()); i++) {
        edge &e = g[u][i];
        int v = g[u][i].to;
        if (dist[v] < 0 && e.f < e.cap) dist[v] = dist[u] + 1, q[qt++] = v;
      }
    }
    return dist[dst] >= 0;
  }
  long long dinic_dfs(int u, long long f) {
    if (u == dst) return f;
    for (int &i = work[u]; i < ((int)g[u].size()); i++) {
      edge &e = g[u][i];
      if (e.cap <= e.f) continue;
      int v = e.to;
      if (dist[v] == dist[u] + 1) {
        long long df = dinic_dfs(v, min(f, e.cap - e.f));
        if (df > 0) {
          e.f += df;
          g[v][e.rev].f -= df;
          return df;
        }
      }
    }
    return 0;
  }
  long long max_flow(int _src, int _dst) {
    src = _src;
    dst = _dst;
    long long result = 0;
    while (dinic_bfs()) {
      fill(work.begin(), work.end(), 0);
      while (long long delta = dinic_dfs(src, 1e8)) result += delta;
    }
    return result;
  }
};
bool isPrime(int k) {
  for (int i = 2; i * i <= k; i++) {
    if (k % i == 0) return false;
  }
  return true;
}
vector<int> g[N];
bool visited[N];
vector<vector<int>> comp;
void dfs(int i) {
  visited[i] = 1;
  comp.back().push_back(i);
  for (auto x : g[i])
    if (!visited[x]) dfs(x);
}
int main() {
  int n;
  cin >> n;
  int a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  Dinic d(n + 2);
  for (int i = 0; i < n; i++) {
    if (a[i] % 2 == 0) {
      d.add_edge(0, i + 1, 2);
      for (int j = 0; j < n; j++)
        if (a[j] % 2 == 1) {
          if (isPrime(a[i] + a[j])) d.add_edge(i + 1, j + 1, 1);
        }
    } else
      d.add_edge(i + 1, n + 1, 2);
  }
  int f = d.max_flow(0, n + 1);
  if (f != n)
    cout << "Impossible" << endl;
  else {
    for (int i = 0; i < n; i++)
      if (a[i] % 2 == 0) {
        for (auto x : d.g[i + 1]) {
          if (x.f == 1) g[i].push_back(x.to - 1), g[x.to - 1].push_back(i);
        }
      }
    for (int i = 0; i < n; i++)
      if (!visited[i]) {
        comp.push_back({});
        dfs(i);
      }
    cout << comp.size() << endl;
    for (auto x : comp) {
      cout << x.size() << " ";
      for (auto y : x) cout << y + 1 << " ";
      cout << endl;
    }
  }
  return 0;
}