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 N = 505;
int source, sink, n, residual[N][N], f, parent[N];
void augment(int u, int flow) {
  if (u == source) {
    f = flow;
  } else if (parent[u] != -1) {
    augment(parent[u], min(flow, residual[parent[u]][u]));
    residual[parent[u]][u] -= f;
    residual[u][parent[u]] += f;
  }
}
bool vis[N];
vector<int> adj[N];
int solve() {
  int ans = 0;
  do {
    for (int i = 0; i < n; ++i) {
      parent[i] = -1;
      vis[i] = false;
    }
    queue<int> q;
    q.push(source);
    vis[source] = true;
    while (!q.empty()) {
      int u = q.front();
      q.pop();
      if (u == sink) {
        break;
      }
      for (int j = 0; j < (int)adj[u].size(); ++j) {
        int v = adj[u][j];
        if (!vis[v] && residual[u][v] > 0) {
          parent[v] = u;
          vis[v] = true;
          q.push(v);
        }
      }
    }
    f = 0;
    augment(sink, 1 << 30);
    ans += f;
  } while (f);
  return ans;
}
bool isprime(int x) {
  for (int i = 2; i * i <= x; ++i) {
    if (x % i == 0) {
      return false;
    }
  }
  return true;
}
vector<int> answer[N];
void dfs(int u, int i, int lado) {
  vis[u] = true;
  answer[i].push_back(u);
  for (int j = 0; j < (int)adj[u].size(); ++j) {
    int v = adj[u][j];
    if (!vis[v] && residual[u][v] == lado) {
      dfs(v, i, !lado);
      break;
    }
  }
}
void add_edge(int a, int b, int valor) {
  adj[a].push_back(b);
  adj[b].push_back(a);
  residual[a][b] += valor;
}
int a[N], x[N], y[N];
int main() {
  int m;
  cin >> m;
  int le = 0, ri = 0;
  for (int i = 0; i < m; ++i) {
    cin >> a[i];
    if (a[i] % 2 == 0) {
      x[le++] = i;
    } else {
      y[ri++] = i;
    }
  }
  if (le != ri) {
    cout << "Impossible" << endl;
    return 0;
  }
  n = m + 2;
  source = m, sink = m + 1;
  for (int i = 0; i < le; i++) {
    add_edge(source, x[i], 2);
    add_edge(y[i], sink, 2);
    for (int j = 0; j < ri; ++j) {
      if (isprime(a[x[i]] + a[y[j]])) {
        add_edge(x[i], y[j], 1);
      }
    }
  }
  if (solve() != 2 * le) {
    cout << "Impossible" << endl;
  } else {
    for (int i = 0; i < n; ++i) {
      vis[i] = false;
    }
    vis[source] = vis[sink] = true;
    int sz = 0;
    for (int i = 0; i < le; ++i) {
      if (!vis[x[i]]) {
        dfs(x[i], sz++, 0);
      }
    }
    cout << sz << endl;
    for (int i = 0; i < sz; ++i) {
      cout << answer[i].size();
      for (int j = 0; j < (int)answer[i].size(); ++j) {
        cout << " " << answer[i][j] + 1;
      }
      cout << endl;
    }
  }
  return 0;
}