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;
struct Edge {
  int from, to, flow, cap;
  Edge(int v, int u, int c) {
    cap = c;
    from = v;
    to = u;
    flow = 0;
  }
  Edge() { flow = to = from = cap = 0; }
};
int s, t;
vector<vector<int> > G;
vector<vector<int> > Grev;
vector<Edge> E;
vector<int> mark;
vector<int> cur;
vector<int> a;
void addEdge(int v, int u, int c) {
  G[v].push_back(E.size());
  E.push_back(Edge(v, u, c));
  G[u].push_back(E.size());
  E.push_back(Edge(u, v, 0));
}
bool dfs1(int v, int t) {
  if (v == t) {
    return 1;
  }
  if (mark[v]) {
    return 0;
  }
  mark[v] = 1;
  for (auto eid : G[v]) {
    int u = E[eid].to;
    if (E[eid].flow < E[eid].cap && dfs1(u, t)) {
      E[eid].flow++;
      E[eid ^ 1].flow--;
      return 1;
    }
  }
  return 0;
}
int isPrime(int n) {
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      return 0;
    }
  }
  return n >= 2;
}
void dfs2(int v) {
  if (a[v] == 0 || mark[v]) {
    return;
  }
  mark[v] = 1;
  cur.push_back(v);
  int p = 1 - 2 * (a[v] % 2);
  for (auto eid : G[v]) {
    int u = E[eid].to;
    if (E[eid].flow == p) {
      dfs2(u);
    }
  }
}
int main() {
  int n;
  cin >> n;
  a.resize(n + 3);
  G.resize(n + 3);
  s = n + 1;
  t = n + 2;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] % 2 == 0) {
      addEdge(s, i, 2);
    } else {
      addEdge(i, t, 2);
    }
  }
  for (int i = 1; i <= n; i++) {
    if (a[i] % 2 == 0) {
      for (int j = 1; j <= n; j++) {
        if (isPrime(a[i] + a[j])) {
          addEdge(i, j, 1);
        }
      }
    }
  }
  for (int i = 0; i < n; i++) {
    mark = vector<int>(n + 3);
    int f = dfs1(s, t);
    if (!f) {
      cout << "Impossible" << endl;
      return 0;
    }
  }
  vector<vector<int> > ans;
  mark = vector<int>(n + 3);
  for (int i = 1; i <= n; i++) {
    cur.clear();
    dfs2(i);
    if (cur.size()) {
      ans.push_back(cur);
    }
  }
  cout << ans.size() << endl;
  for (auto b : ans) {
    cout << b.size() << " ";
    for (auto x : b) {
      cout << x << " ";
    }
    cout << endl;
  }
  return 0;
}