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 = int(1e9);
bool isprime(int n) {
  assert(n > 2);
  for (int i = 2; i * i <= n; ++i)
    if (n % i == 0) return false;
  return true;
}
vector<size_t> bfs(const vector<vector<int> >& g, size_t source, size_t sink,
                   int& dflow) {
  const size_t NO_NODE = g.size();
  queue<size_t> q;
  q.push(source);
  vector<int> fl(g.size(), 0);
  fl[source] = oo;
  vector<size_t> parent(g.size(), NO_NODE);
  while (!q.empty()) {
    size_t u = q.front();
    q.pop();
    for (size_t v = 0; v < g.size(); ++v) {
      int flow = min(fl[u], g[u][v]);
      if (flow > fl[v]) {
        fl[v] = flow;
        parent[v] = u;
        q.push(v);
      }
    }
  }
  dflow = fl[sink];
  if (dflow == 0) {
    return vector<size_t>();
  }
  vector<size_t> ret;
  for (size_t v = sink; v != source; v = parent[v]) {
    assert(v < NO_NODE);
    ret.push_back(v);
  }
  ret.push_back(source);
  return ret;
}
template <typename T>
void pprint(const vector<vector<T> >& g) {
  for (size_t i = 0; i < g.size(); ++i) {
    for (size_t j = 0; j < g[i].size(); ++j) {
      std::cout << g[i][j] << " ";
    }
    std::cout << std::endl;
  }
}
static vector<vector<int> > f;
int max_flow(vector<vector<int> >& g, size_t source, size_t sink) {
  int flow = 0;
  f = vector<vector<int> >(g.size(), vector<int>(g[0].size()));
  for (;;) {
    int dflow;
    vector<size_t> path = bfs(g, source, sink, dflow);
    if (dflow == 0) break;
    for (size_t i = 0; i + 1 < path.size(); ++i) {
      size_t u = path[i], v = path[i + 1];
      f[v][u] += dflow;
      f[u][v] -= dflow;
      g[u][v] += dflow;
      g[v][u] -= dflow;
    }
    flow += dflow;
  }
  return flow;
}
vector<int> input() {
  using std::cin;
  size_t n;
  cin >> n;
  vector<int> w(n);
  for (size_t i = 0; i < n; ++i) cin >> w[i];
  return w;
}
vector<size_t> dfs(const vector<vector<int> >& g, size_t u,
                   vector<bool>& visited) {
  vector<size_t> ans;
  visited[u] = true;
  for (size_t v = 0; v < g[u].size(); ++v) {
    if (g[u][v] != 0 && !visited[v]) {
      ans = dfs(g, v, visited);
      ans.push_back(u);
      return ans;
    }
  }
  return vector<size_t>(1, u);
}
int main() {
  vector<int> w = input();
  vector<vector<int> > rem(2), ids(2);
  for (size_t i = 0; i < w.size(); ++i) {
    rem[w[i] % 2].push_back(w[i]);
    ids[w[i] % 2].push_back(i + 1);
  }
  if (rem[0].size() != rem[1].size()) {
    cout << "Impossible" << endl;
    return 0;
  }
  const size_t sz = rem[0].size(), source = 2 * sz, sink = source + 1;
  vector<vector<int> > g(sink + 1, vector<int>(sink + 1, 0));
  for (size_t i = 0; i < sz; ++i) {
    g[source][i] = 2;
    g[sz + i][sink] = 2;
  }
  for (size_t i = 0; i < sz; ++i) {
    for (size_t j = 0; j < sz; ++j) {
      int w1 = rem[0][i], w2 = rem[1][j];
      if (isprime(w1 + w2)) g[i][sz + j] = 1;
    }
  }
  int flow = max_flow(g, source, sink);
  if (size_t(flow) != w.size()) {
    cout << "Impossible" << endl;
    return 0;
  }
  for (size_t i = 0; i < 2 * sz; ++i) {
    f[i].pop_back();
    f[i].pop_back();
    for (size_t j = 0; j < f[i].size(); ++j)
      if (f[i][j] != 0) f[i][j] = 1;
  }
  f.pop_back();
  f.pop_back();
  vector<vector<size_t> > ans;
  vector<bool> visited(f.size(), false);
  for (size_t i = 0; i < f.size(); ++i) {
    if (!visited[i]) {
      ans.push_back(dfs(f, i, visited));
    }
  }
  for (size_t i = 0; i < ans.size(); ++i) assert(ans[i].size() > 2);
  cout << ans.size() << endl;
  for (size_t i = 0; i < ans.size(); ++i) {
    cout << ans[i].size() << " ";
    for (size_t j = 0; j < ans[i].size(); ++j) {
      size_t v = ans[i][j];
      cout << ids[v / sz][v % sz] << " ";
    }
    cout << endl;
  }
  return 0;
}