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 MAXN = 210, MAXA = 20010;
void kill(bool b) {
  if (b) {
    puts("Impossible");
    exit(0);
  }
}
int N, A[MAXN];
bool isprime[MAXA];
int cap[MAXN][MAXN];
vector<int> adj[MAXN];
vector<vector<int> > ans;
bool vis[MAXN];
void add(int x, int y, int v) {
  adj[x].push_back(y);
  adj[y].push_back(x);
  cap[x][y] = v;
}
bool dfs(int s, int t) {
  if (s == t) {
    return true;
  }
  if (vis[s]) {
    return false;
  }
  vis[s] = true;
  for (__typeof((adj[s]).begin()) it = (adj[s]).begin(); it != (adj[s]).end();
       it++) {
    int v = *it;
    if (cap[s][v] && dfs(v, t)) {
      cap[s][v]--;
      cap[v][s]++;
      return true;
    }
  }
  return false;
}
int main() {
  if (fopen("input.txt", "r")) {
    freopen("input.txt", "r", stdin);
  }
  ios::sync_with_stdio(false);
  cin >> N;
  int nodd = 0, neven = 0;
  for (int i = 1; i <= N; i++) {
    cin >> A[i];
    if (A[i] % 2) {
      add(i, N + 1, 2);
      nodd++;
    } else {
      add(0, i, 2);
      neven++;
    }
  }
  kill(nodd != neven);
  memset((isprime), (true), sizeof(isprime));
  for (int i = 2; i < MAXA; i++) {
    for (int j = 2; j * j <= i; j++) {
      if (i % j == 0) {
        isprime[i] = false;
        break;
      }
    }
  }
  for (int i = 1; i <= N; i++) {
    for (int j = i + 1; j <= N; j++) {
      if (!isprime[A[i] + A[j]]) {
        continue;
      }
      int a = i, b = j;
      if (A[i] % 2) {
        swap(a, b);
      }
      add(a, b, 1);
    }
  }
  int flow = 0;
  while (dfs(0, N + 1)) {
    flow++;
    memset((vis), (false), sizeof(vis));
  }
  kill(flow != N);
  for (int i = 1; i <= N; i++) {
    adj[i].clear();
  }
  for (int i = 1; i <= N; i++) {
    for (int j = i + 1; j <= N; j++) {
      if (!isprime[A[i] + A[j]]) {
        continue;
      }
      int a = i, b = j;
      if (A[i] % 2) {
        swap(a, b);
      }
      if (cap[b][a] == 1) {
        adj[a].push_back(b);
        adj[b].push_back(a);
      }
    }
  }
  for (int i = 1; i <= N; i++) {
    assert(adj[i].size() == 2);
  }
  memset((vis), (false), sizeof(vis));
  for (int i = 1; i <= N; i++) {
    if (!vis[i]) {
      int x = i;
      vector<int> cyc;
      while (true) {
        vis[x] = true;
        cyc.push_back(x);
        bool found = false;
        for (__typeof((adj[x]).begin()) it = (adj[x]).begin();
             it != (adj[x]).end(); it++) {
          int t = *it;
          if (!vis[t]) {
            x = t;
            found = true;
            break;
          }
        }
        if (!found) {
          break;
        }
      }
      ans.push_back(cyc);
    }
  }
  cout << ans.size() << '\n';
  for (__typeof((ans).begin()) it = (ans).begin(); it != (ans).end(); it++) {
    vector<int> &v = *it;
    cout << v.size() << ' ';
    for (__typeof((v).begin()) jt = (v).begin(); jt != (v).end(); jt++) {
      cout << *jt << ' ';
    }
    cout << '\n';
  }
}