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;
constexpr int INF = 1e9;
int n;
vector<pair<int, int> > graf[505];
int c[200005], odl[505], nxt[505], tab[505];
bool isComp[20004];
int id;
int s, t;
int res;
vector<int> gt[505];
vector<vector<int> > cykle;
bool vis[505];
void genPrimes() {
  for (int i = 2; i * i <= 20000; i++)
    if (!isComp[i]) {
      for (int j = i * i; j <= 20000; j += i) isComp[j] = true;
    }
}
void dfs(int a) {
  vis[a] = true;
  cykle.back().push_back(a);
  for (auto e : gt[a])
    if (!vis[e]) dfs(e);
}
void addEdge(int a, int b, int v) {
  graf[a].push_back({b, id});
  c[id++] = v;
  graf[b].push_back({a, id++});
}
bool bfs() {
  for (int i = 0; i <= t; i++) odl[i] = INF;
  odl[s] = 0;
  queue<int> q;
  q.push(s);
  while (!q.empty()) {
    int w = q.front();
    q.pop();
    for (auto e : graf[w]) {
      if (c[e.second] == 0) continue;
      if (odl[e.first] == INF) {
        odl[e.first] = odl[w] + 1;
        q.push(e.first);
      }
    }
  }
  return odl[t] != INF;
}
int przeplyn(int a, int ogr) {
  if (ogr == 0 || a == t) return ogr;
  int res = 0;
  for (int i = nxt[a]; i < (int)(graf[a]).size(); i++) {
    auto e = graf[a][i];
    if (odl[e.first] != odl[a] + 1) continue;
    int ile = przeplyn(e.first, min(ogr, c[e.second]));
    ogr -= ile;
    c[e.second] -= ile;
    c[e.second ^ 1] += ile;
    res += ile;
    if (ogr == 0) break;
  }
  return res;
}
int dinic() {
  int res = 0;
  while (bfs()) {
    for (int i = 0; i <= t; i++) nxt[i] = 0;
    res += przeplyn(s, INF);
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  s = 0;
  t = n + 1;
  vector<int> odd, even;
  for (int i = 1; i <= n; i++) {
    cin >> tab[i];
    if (tab[i] & 1)
      odd.push_back(i);
    else
      even.push_back(i);
  }
  genPrimes();
  for (auto a : odd)
    for (auto b : even) {
      if (!isComp[tab[a] + tab[b]]) {
        addEdge(a, b, 1);
      }
    }
  for (auto a : odd) addEdge(0, a, 2);
  for (auto b : even) addEdge(b, t, 2);
  int res = dinic();
  if (res != n || (int)(even).size() != (int)(odd).size()) {
    cout << "Impossible\n";
    exit(0);
  }
  for (auto a : even) {
    for (auto e : graf[a]) {
      if ((e.second & 1) && c[e.second]) {
        gt[e.first].push_back(a);
        gt[a].push_back(e.first);
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    if (!vis[i]) {
      cykle.push_back(vector<int>());
      dfs(i);
    }
  }
  cout << (int)(cykle).size() << "\n";
  for (auto v : cykle) {
    cout << (int)(v).size() << " ";
    for (auto a : v) {
      cout << a << " ";
    }
    cout << "\n";
  }
  return 0;
}