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;
bool is_prime[100000];
void set_prime() {
  fill(is_prime, is_prime + 100000, true);
  is_prime[0] = is_prime[1] = false;
  for (int i = 2; i * i < 100000; i++) {
    if (!is_prime[i]) continue;
    for (int j = i * i; j < 100000; j += i) is_prime[j] = false;
  }
}
vector<int> even, odd;
vector<int> v[300], e[300];
int pr[300];
bool visit[300];
bool hv[300];
int N;
int A[300];
vector<int> p, q;
bool find(int x) {
  visit[x] = true;
  for (int vi = 0; vi < v[x].size(); vi++) {
    int p = pr[v[x][vi]];
    if (!p || !visit[p] && find(p)) {
      pr[x] = v[x][vi];
      pr[v[x][vi]] = x;
      return true;
    }
  }
  return false;
}
int main() {
  set_prime();
  scanf("%d", &N);
  for (int Ni = 1; Ni <= N; Ni++) {
    scanf("%d", &A[Ni]);
    if (A[Ni] % 2 == 0)
      even.push_back(Ni);
    else
      odd.push_back(Ni);
  }
  if (even.size() != odd.size()) {
    puts("Impossible");
    return 0;
  }
  fill(pr, pr + 300, 0);
  for (int i = 0; i < odd.size(); i++) {
    for (int j = 0; j < even.size(); j++) {
      int a = A[odd[i]];
      int b = A[even[j]];
      if (is_prime[a + b]) v[i + 1].push_back(j + odd.size() + 1);
    }
  }
  for (int i = 1; i <= odd.size(); i++) {
    fill(visit, visit + 300, false);
    if (!find(i)) {
      puts("Impossible");
      return 0;
    }
  }
  for (int i = 1; i <= odd.size(); i++) {
    int a = i - 1;
    int b = pr[i] - odd.size() - 1;
    e[odd[a]].push_back(even[b]);
    v[i].erase(find(v[i].begin(), v[i].end(), pr[i]));
  }
  fill(pr, pr + 300, 0);
  for (int i = 1; i <= odd.size(); i++) {
    fill(visit, visit + 300, false);
    if (!find(i)) {
      puts("Impossible");
      return 0;
    }
  }
  for (int i = 1; i <= odd.size(); i++) {
    int a = i - 1;
    int b = pr[i] - odd.size() - 1;
    e[even[b]].push_back(odd[a]);
  }
  vector<vector<int> > Ans;
  for (int Ni = 1; Ni <= N; Ni++) {
    if (hv[Ni]) continue;
    vector<int> t;
    int p = Ni;
    while (1) {
      t.push_back(p);
      hv[p] = true;
      if (e[p][0] == t[0]) break;
      p = e[p][0];
    }
    Ans.push_back(t);
  }
  printf("%d\n", Ans.size());
  for (int Ai = 0; Ai < Ans.size(); Ai++) {
    vector<int> &t = Ans[Ai];
    printf("%d", t.size());
    for (int ti = 0; ti < t.size(); ti++) printf(" %d", t[ti]);
    puts("");
  }
}