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;
int a[201];
bool isprime[20005];
vector<int> nb[205];
int s = 202, t = 203;
int c[205][205];
int f[205][205];
int parent[205];
bool vis[205];
int flow;
int even, odd;
int tables = 0;
vector<int> table[205];
bool BFS() {
  queue<int> q;
  int i, j, v;
  for (i = 1; i < 205; i++) {
    parent[i] = 0;
    vis[i] = false;
  }
  q.push(s);
  vis[s] = true;
  while (!q.empty() && !vis[t]) {
    v = q.front();
    q.pop();
    for (i = 0; i < nb[v].size(); i++) {
      if (!vis[nb[v][i]] && c[v][nb[v][i]] - f[v][nb[v][i]] > 0) {
        vis[nb[v][i]] = true;
        parent[nb[v][i]] = v;
        q.push(nb[v][i]);
      }
    }
  }
  return vis[t];
}
void update_flow() {
  int u, v;
  int minflow = INT_MAX;
  v = t;
  while (v != s) {
    u = parent[v];
    if (c[u][v] - f[u][v] < minflow) minflow = c[u][v] - f[u][v];
    v = parent[v];
  }
  v = t;
  while (v != s) {
    u = parent[v];
    f[u][v] += minflow;
    f[v][u] -= minflow;
    v = parent[v];
  }
  flow += minflow;
}
void DFS(int v) {
  int i;
  vis[v] = true;
  table[tables].push_back(v);
  for (i = 0; i < nb[v].size(); i++) {
    if (f[v][nb[v][i]] != 0 && !vis[nb[v][i]]) DFS(nb[v][i]);
  }
}
int main() {
  int i, j;
  cin >> n;
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (i = 1; i <= 20005; i++) isprime[i] = true;
  for (i = 2; i <= 20005; i++) {
    if (isprime[i])
      for (j = i + i; j <= 20005; j = j + i) isprime[j] = false;
  }
  for (i = 1; i <= n; i++) {
    if (a[i] % 2 == 1) {
      nb[s].push_back(i);
      nb[i].push_back(s);
      c[s][i] = 2;
      odd++;
    } else {
      nb[t].push_back(i);
      nb[i].push_back(t);
      c[i][t] = 2;
      even++;
    }
  }
  if (even != odd) {
    cout << "Impossible" << endl;
    return 0;
  }
  for (i = 1; i <= n; i++)
    for (j = i + 1; j <= n; j++) {
      if (isprime[a[i] + a[j]]) {
        nb[i].push_back(j);
        nb[j].push_back(i);
        if (a[i] % 2 == 1)
          c[i][j] = 1;
        else
          c[j][i] = 1;
      }
    }
  while (BFS()) update_flow();
  if (flow != n) {
    cout << "Impossible" << endl;
    return 0;
  }
  for (i = 1; i < 205; i++) vis[i] = false;
  vis[s] = true;
  vis[t] = true;
  for (i = 1; i <= n; i++) {
    if (!vis[i]) {
      tables++;
      DFS(i);
    }
  }
  cout << tables << endl;
  for (i = 1; i <= tables; i++) {
    cout << table[i].size() << " ";
    for (j = 0; j < table[i].size(); j++) cout << table[i][j] << " ";
    cout << endl;
  }
  return 0;
}