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 INT_INF = 2e9;
bool is_prime(int n) {
  for (int i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
void dfs(vector<vector<int> > &gr, vector<int> &path, vector<bool> &vis,
         int v) {
  if (vis[v]) return;
  path.push_back(v);
  vis[v] = true;
  for (auto u : gr[v]) dfs(gr, path, vis, u);
}
int maxflow_dfs(vector<vector<pair<int, int> > > &gr, vector<int> &path,
                vector<bool> &vis, int s, int t) {
  if (s == t) {
    path.push_back(s);
    return INT_INF;
  }
  if (vis[s]) return 0;
  vis[s] = true;
  int flow_size;
  for (auto e : gr[s]) {
    if (e.second > 0) {
      if (flow_size = maxflow_dfs(gr, path, vis, e.first, t)) {
        path.push_back(s);
        return min(flow_size, e.second);
      }
    }
  }
  return 0;
}
int maxflow(vector<vector<pair<int, int> > > &gr, int s, int t) {
  vector<int> path;
  vector<bool> vis(((int)gr.size()));
  int flow_size;
  int ans = 0;
  while (flow_size = maxflow_dfs(gr, path, vis, s, t)) {
    ans += flow_size;
    reverse(path.begin(), path.end());
    for (int i = 1; i < ((int)path.size()); i++) {
      for (auto &e : gr[path[i - 1]])
        if (e.first == path[i]) e.second -= flow_size;
      for (auto &e : gr[path[i]])
        if (e.first == path[i - 1]) e.second += flow_size;
    }
    path.clear();
    vis = vector<bool>(((int)gr.size()));
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  vector<vector<pair<int, int> > > gr(n + 2);
  for (int i = 0; i < n; i++) {
    if (a[i] % 2 == 0)
      gr[i].emplace_back(n + 1, 2);
    else
      gr[n].emplace_back(i, 2);
    for (int j = i + 1; j < n; j++) {
      if (a[i] % 2 != a[j] % 2 && is_prime(a[i] + a[j]))
        gr[i].emplace_back(j, a[i] % 2), gr[j].emplace_back(i, a[j] % 2);
    }
  }
  int mf = maxflow(gr, n, n + 1);
  if (mf == n) {
    vector<vector<int> > gr_norm(n);
    for (int i = 0; i < n; i++) {
      for (auto e : gr[i]) {
        if (e.first < n && e.second != (a[i] % 2))
          gr_norm[i].push_back(e.first);
      }
    }
    vector<vector<int> > paths;
    vector<bool> vis(n);
    vector<int> path;
    for (int i = 0; i < n; i++) {
      dfs(gr_norm, path, vis, i);
      if (((int)path.size()) > 0) paths.push_back(path);
      path.clear();
    }
    cout << ((int)paths.size()) << endl;
    for (auto path : paths) {
      cout << ((int)path.size());
      for (auto el : path) cout << ' ' << el + 1;
      cout << endl;
    }
  } else {
    cout << "Impossible" << endl;
  }
}