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;
int N;
vector<int> A, odd, even;
vector<vector<int> > C, flow, neigh;
bool isPrime(int n) {
  for (int i = 2; i < n; i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
int edmondsKarp(int s, int t) {
  flow = vector<vector<int> >(N + 2, vector<int>(N + 2, 0));
  vector<int> pre, aug;
  while (true) {
    queue<int> q;
    q.push(s);
    pre = vector<int>(N + 2, -1);
    pre[s] = s;
    aug = vector<int>(N + 2, INT_MAX);
    bool augFound = false;
    while (!q.empty() && !augFound) {
      int u = q.front();
      q.pop();
      for (int i = 0; i < (int)(neigh[u].size()); ++i) {
        int v = neigh[u][i];
        if (C[u][v] - flow[u][v] > 0 && pre[v] == -1) {
          aug[v] = min(C[u][v] - flow[u][v], aug[u]);
          pre[v] = u;
          if (v != t) q.push(v);
          if (v == t) {
            while (pre[v] != v) {
              u = pre[v];
              flow[u][v] += aug[t];
              flow[v][u] -= aug[t];
              v = u;
            }
            augFound = true;
            break;
          }
        }
      }
    }
    if (pre[t] == -1) {
      int sum = 0;
      for (int i = 0; i < (int)(neigh[s].size()); ++i)
        sum += flow[s][neigh[s][i]];
      return sum;
    }
  }
  return 0;
}
int main() {
  cin >> N;
  A = vector<int>(N, 0);
  for (int i = 0; i < (int)(N); ++i) cin >> A[i];
  C = vector<vector<int> >(N + 2, vector<int>(N + 2, 0));
  neigh = vector<vector<int> >(N + 2, vector<int>(0, 0));
  for (int i = 0; i < (int)(N); ++i) {
    if (A[i] % 2 == 0)
      even.push_back(i);
    else
      odd.push_back(i);
    for (int j = 0; j < (int)(i); ++j) {
      if (isPrime(A[i] + A[j])) {
        if (A[i] % 2 == 0) {
          C[i][j] = 1;
          neigh[i].push_back(j);
          neigh[j].push_back(i);
        } else {
          C[j][i] = 1;
          neigh[j].push_back(i);
          neigh[i].push_back(j);
        }
      }
    }
  }
  if (odd.size() != even.size()) {
    cout << "Impossible" << endl;
    return 0;
  }
  for (int i = 0; i < (int)(even.size()); ++i) {
    int k = even[i];
    C[N][k] = 2;
    neigh[N].push_back(k);
    neigh[k].push_back(N);
  }
  for (int i = 0; i < (int)(odd.size()); ++i) {
    int k = odd[i];
    C[k][N + 1] = 2;
    neigh[N + 1].push_back(k);
    neigh[k].push_back(N + 1);
  }
  int fl = edmondsKarp(N, N + 1);
  if (fl != N) {
    cout << "Impossible" << endl;
    return 0;
  }
  vector<int> g[300];
  for (int i = 0; i < (int)(N); ++i)
    for (int j = 0; j < (int)(i); ++j) {
      if (flow[i][j] != 0) {
        g[i].push_back(j);
        g[j].push_back(i);
      }
    }
  vector<vector<int> > cycles;
  vector<int> vis = vector<int>(N, 0);
  for (int i = 0; i < (int)(N); ++i) {
    if (vis[i] == 0) {
      vector<int> cycle;
      int p = i, n = g[i][0];
      cycle.push_back(i);
      while (n != i) {
        vis[n] = 1;
        cycle.push_back(n);
        int t = 0;
        while (g[n][t] == p) t++;
        p = n;
        n = g[n][t];
      }
      cycles.push_back(cycle);
    }
  }
  cout << cycles.size() << endl;
  for (int i = 0; i < (int)(cycles.size()); ++i) {
    cout << cycles[i].size();
    for (int j = 0; j < (int)(cycles[i].size()); ++j) {
      cout << " " << cycles[i][j] + 1;
    }
    cout << endl;
  }
  return 0;
}