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 unsigned long long maxn = 310;
const unsigned long long inf = 1e9 + 500;
const unsigned long long mod = 1e9 + 7;
const unsigned long long maxm = 2e4 + 500;
unsigned long long a[maxn];
unsigned long long id[maxn];
vector<unsigned long long> ger[maxn];
bool npr[maxm];
bool vis[maxn];
unsigned long long match[maxn][2];
bool tt;
bool dfs(unsigned long long a) {
  vis[a] = 1;
  for (auto u : ger[a]) {
    if (match[u][tt] == -1 || (!vis[match[u][tt]] && dfs(match[u][tt]))) {
      match[a][tt] = u;
      match[u][tt] = a;
      return 1;
    }
  }
  return 0;
}
vector<unsigned long long> vec[maxn];
unsigned long long cnr;
void dfss(unsigned long long a) {
  vis[a] = 1;
  vec[cnr].push_back(a + 1);
  unsigned long long v = match[a][0];
  unsigned long long u = match[a][1];
  if (vis[v] == 0) {
    dfss(v);
  }
  if (vis[u] == 0) {
    dfss(u);
  }
}
int main() {
  for (unsigned long long i = 2; i <= maxm; i++) {
    for (unsigned long long j = i * 2; j < maxm; j += i) {
      npr[j] = 1;
    }
  }
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  unsigned long long n;
  cin >> n;
  unsigned long long bala = 0;
  for (unsigned long long i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] & 1) {
      bala++;
    } else {
      bala--;
    }
  }
  if (bala != 0) {
    cout << "Impossible";
    return 0;
  }
  for (unsigned long long i = 0; i < n; i++) {
    for (unsigned long long j = i + 1; j < n; j++) {
      if (!npr[a[i] + a[j]]) {
        ger[i].push_back(j);
        ger[j].push_back(i);
      }
    }
  }
  tt = 0;
  for (unsigned long long i = 0; i < maxn; i++) {
    match[i][tt] = -1;
  }
  for (unsigned long long i = 0; i < n; i++) {
    if (a[i] & 1) {
      fill(vis, vis + maxn, 0);
      dfs(i);
    }
  }
  for (unsigned long long i = 0; i < n; i++) {
    ger[i].clear();
    if (match[i][tt] == -1) {
      cout << "Impossible";
      return 0;
    }
  }
  for (unsigned long long i = 0; i < n; i++) {
    for (unsigned long long j = i + 1; j < n; j++) {
      if (!npr[a[i] + a[j]] && match[i][0] != j && match[j][0] != i) {
        ger[i].push_back(j);
        ger[j].push_back(i);
      }
    }
  }
  tt = 1;
  for (unsigned long long i = 0; i < maxn; i++) {
    match[i][tt] = -1;
  }
  for (unsigned long long i = 0; i < n; i++) {
    if (a[i] & 1) {
      fill(vis, vis + maxn, 0);
      dfs(i);
    }
  }
  for (unsigned long long i = 0; i < n; i++) {
    ger[i].clear();
    if (match[i][tt] == -1) {
      cout << "Impossible";
      return 0;
    }
  }
  fill(vis, vis + maxn, 0);
  for (unsigned long long i = 0; i < n; i++) {
    if (vis[i] == 0) {
      dfss(i);
      cnr++;
    }
  }
  cout << cnr << endl;
  for (unsigned long long i = 0; i < cnr; i++) {
    cout << vec[i].size() << ' ';
    for (auto a : vec[i]) {
      cout << a << ' ';
    }
    cout << endl;
  }
}