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, m;
int p[500];
int g[500][500], f[500][500];
vector<int> prime[101], edge[101], num[101];
int bfs(int g[][500], int f[][500], int src, int sink) {
  int m[6400], u, v;
  for (int i = 0; i < N; i++) {
    p[i] = -1;
  }
  p[src] = -2;
  m[src] = INT_MAX;
  queue<int> q;
  q.push(src);
  while (!q.empty()) {
    u = q.front();
    q.pop();
    for (v = 0; v < N; v++) {
      if (g[u][v] - f[u][v] > 0 && p[v] == -1) {
        p[v] = u;
        m[v] = min(m[u], g[u][v] - f[u][v]);
        if (v != sink) {
          q.push(v);
        } else {
          return m[sink];
        }
      }
    }
  }
  return 0;
}
int max_flow(int g[][500], int f[][500], int src, int sink) {
  int m = 0;
  int flow = 0;
  while (1) {
    m = bfs(g, f, src, sink);
    if (m == 0) {
      break;
    } else {
      flow += m;
      int v = sink, u;
      while (v != src) {
        u = p[v];
        f[u][v] += m;
        f[v][u] -= m;
        v = u;
      }
    }
  }
  return flow;
}
int isprime(int x) {
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      return 0;
    }
  }
  return 1;
}
int vis[100000];
int numbr;
int esize, osize;
vector<int> even, odd, evenidx, oddidx, numv;
void dfs(int root, int prev, int print = 0) {
  vis[root + 1] = 1;
  if (print) {
    if (root < esize)
      cout << evenidx[root] << " ";
    else
      cout << oddidx[root - esize] << " ";
  }
  numbr++;
  for (int i = 1; i <= osize + esize + 1; i++) {
    if (i - 1 == prev) continue;
    if (f[root + 1][i] == 1 && vis[i] == 0) {
      dfs(i - 1, root, print);
    }
  }
}
int main() {
  int n;
  cin >> n;
  int a[1000];
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    if (a[i] % 2 == 0) {
      even.push_back(a[i]);
      evenidx.push_back(i + 1);
    } else {
      odd.push_back(a[i]);
      oddidx.push_back(i + 1);
    }
  }
  esize = even.size();
  osize = odd.size();
  for (int i = 0; i < even.size(); i++) {
    for (int j = 0; j < odd.size(); j++) {
      if (isprime(even[i] + odd[j])) {
        g[i + 1][esize + j + 1] = 1;
      }
    }
  }
  for (int i = 0; i < esize; i++) {
    g[0][i + 1] = 2;
  }
  for (int i = 0; i < osize; i++) {
    g[esize + i + 1][esize + osize + 1] = 2;
  }
  N = esize + osize + 2;
  int fans = 0;
  fans = max_flow(g, f, 0, N - 1);
  if (fans < n) {
    cout << "Impossible";
    return 0;
  }
  for (int i = 1; i < N; i++) {
    for (int j = 1; j < N; j++) {
      if (f[i][j] == 1) {
        f[j][i] = 1;
      }
    }
  }
  for (int i = 0; i < esize + osize + 1; i++) {
    vis[i] = 0;
  }
  int ct = 0;
  for (int i = 0; i < esize; i++) {
    if (vis[i + 1] == 0) {
      ct++;
      numbr = 0;
      dfs(i, -1, 0);
      numv.push_back(numbr);
    }
  }
  for (int i = 0; i < esize + osize + 1; i++) {
    vis[i] = 0;
  }
  cout << ct << endl;
  int k = 0;
  for (int i = 0; i < esize; i++) {
    if (vis[i + 1] == 0) {
      numbr = 0;
      cout << numv[k] << " ";
      k++;
      dfs(i, -1, 1);
      cout << endl;
    }
  }
  return 0;
}