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 nmax = 205;
int n, v[nmax], c[nmax][nmax], f[nmax][nmax], t[nmax], a, b, cnt;
bool viz[nmax];
vector<int> G[nmax], ans[nmax];
bool bfs() {
  memset(viz, 0, sizeof viz);
  queue<int> coada;
  coada.push(0);
  viz[0] = true;
  while (!coada.empty()) {
    int nod = coada.front();
    coada.pop();
    if (nod == 201) continue;
    for (auto it : G[nod]) {
      if (viz[it] == true || f[nod][it] == c[nod][it]) continue;
      coada.push(it);
      viz[it] = true;
      t[it] = nod;
    }
  }
  return viz[201];
}
void Find(int nod) {
  viz[nod] = true;
  ans[cnt].push_back(nod);
  for (auto it : G[nod]) {
    if (it == 0 || it == 201 || viz[it] == true || abs(f[nod][it]) != 1)
      continue;
    Find(it);
    return;
  }
}
bool isPrim(int x) {
  if (x == 2) return true;
  if (x % 2 == 0) return false;
  for (int i = 3; i * i <= x; i += 2) {
    if (x % i == 0) {
      return false;
    }
  }
  return true;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> v[i];
    if (v[i] % 2 == 0) {
      ++a;
      for (int j = i - 1; j >= 1; --j) {
        if (v[j] % 2 == 1 && isPrim(v[j] + v[i])) {
          c[i][j] = 1;
          G[i].push_back(j);
          G[j].push_back(i);
        }
      }
      c[0][i] = 2;
      G[0].push_back(i);
      G[i].push_back(0);
    } else {
      ++b;
      for (int j = i - 1; j >= 1; --j) {
        if (v[j] % 2 == 0 && isPrim(v[j] + v[i])) {
          c[j][i] = 1;
          G[i].push_back(j);
          G[j].push_back(i);
        }
      }
      c[i][201] = 2;
      G[i].push_back(201);
      G[201].push_back(i);
    }
  }
  if (a != b) {
    cout << "Impossible";
    return 0;
  }
  int flow, fmin;
  for (flow = 0; bfs();) {
    for (auto it : G[201]) {
      if (!viz[it] || f[it][201] == c[it][201]) continue;
      fmin = 1e9;
      t[201] = it;
      for (int nod = 201; nod != 0; nod = t[nod]) {
        fmin = min(fmin, c[t[nod]][nod] - f[t[nod]][nod]);
      }
      if (fmin == 0) continue;
      for (int nod = 201; nod != 0; nod = t[nod]) {
        f[t[nod]][nod] += fmin;
        f[nod][t[nod]] -= fmin;
      }
      flow += fmin;
    }
  }
  if (flow != 2 * a) {
    cout << "Impossible";
    return 0;
  }
  memset(viz, 0, sizeof viz);
  for (int i = 1; i <= n; ++i) {
    if (viz[i] == false) {
      ++cnt;
      Find(i);
    }
  }
  cout << cnt << "\n";
  for (int i = 1; i <= cnt; ++i) {
    cout << ans[i].size() << " ";
    for (auto it : ans[i]) {
      cout << it << " ";
    }
    cout << "\n";
  }
  return 0;
}