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 INF = numeric_limits<int>::max() - 1;
bool prime[(int)1e5 + 5];
void genPrime() {
  memset(prime, true, sizeof(prime));
  for (int i = 2; i < 1e5 + 5; i++) {
    if (!prime[i]) continue;
    for (long long j = i * (long long)i; j < 1e5 + 5; j += i) {
      prime[j] = false;
    }
  }
}
const int N = 205;
int a[N], g[N][N], go[N][N], n, even;
bool w[N][N];
int p[N];
queue<int> q;
bitset<N> us;
bool bfs() {
  while (!q.empty()) q.pop();
  us.reset();
  q.push(0);
  us[0] = true;
  while (!q.empty()) {
    int cur = q.front();
    q.pop();
    if (cur == n + 1) return true;
    for (int i = 0; i <= n + 1; i++) {
      if (g[cur][i] && !us[i]) {
        us[i] = true;
        p[i] = cur;
        q.push(i);
      }
    }
  }
  return false;
}
int maxFlow() {
  int res = 0;
  while (bfs()) {
    int cur = INF;
    for (int i = n + 1; i != 0; i = p[i]) cur = min(g[p[i]][i], cur);
    for (int i = n + 1; i != 0; i = p[i]) {
      g[p[i]][i] -= cur;
      g[i][p[i]] += cur;
    }
    res += cur;
  }
  return res;
}
void genNew() {
  while (!q.empty()) q.pop();
  us.reset();
  for (int i = 1; i <= n; i++) {
    if (us[i]) continue;
    q.push(i);
    us[i] = true;
    while (!q.empty()) {
      int cur = q.front();
      q.pop();
      for (int j = 1; j <= n; j++) {
        if (go[i][j] - g[i][j] > 0) {
          w[i][j] = w[j][i] = true;
          if (!us[j]) {
            q.push(j);
            us[j] = true;
          }
        }
      }
    }
  }
}
vector<vector<int> > ans;
void printCycle(int v) {
  us[v] = true;
  ans.back().push_back(v);
  for (int i = 1; i <= n; i++) {
    if (w[v][i] && !us[i]) {
      printCycle(i);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  genPrime();
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] & 1)
      g[0][i] = 2;
    else
      g[i][n + 1] = 2, even++;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if ((a[i] & 1) != 0 && (a[j] & 1) == 0) {
        if (prime[a[i] + a[j]]) {
          g[i][j] = go[i][j] = 1;
        }
      }
    }
  }
  if (maxFlow() != even * 2) {
    cout << "Impossible" << endl;
    return 0;
  }
  genNew();
  us.reset();
  for (int i = 1; i <= n; i++) {
    if (!us[i]) {
      ans.push_back(vector<int>());
      printCycle(i);
    }
  }
  cout << ans.size() << endl;
  for (size_t i = 0; i < ans.size(); i++) {
    cout << ans[i].size() << " ";
    for (size_t j = 0; j < ans[i].size(); j++) {
      cout << ans[i][j] << " ";
    }
    cout << endl;
  }
  return 0;
}