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;
template <class T>
struct Dinic {
  static const int MAXV = 10000;
  static const T INF = 0x3f3f3f3f;
  struct Edge {
    int v;
    T f;
    int re;
    Edge(int _v, T _f, int _re) : v(_v), f(_f), re(_re) {}
  };
  int n, s, t, level[MAXV];
  vector<Edge> E[MAXV];
  int now[MAXV];
  Dinic(int _n, int _s, int _t) : n(_n), s(_s), t(_t) {}
  void add_edge(int u, int v, T f, bool bidirectional = false) {
    E[u].emplace_back(v, f, E[v].size());
    E[v].emplace_back(u, 0, E[u].size() - 1);
    if (bidirectional) {
      E[v].emplace_back(u, f, E[u].size() - 1);
    }
  }
  bool BFS() {
    memset(level, -1, sizeof(level));
    queue<int> que;
    que.emplace(s);
    level[s] = 0;
    while (not que.empty()) {
      int u = que.front();
      que.pop();
      for (auto it : E[u]) {
        if (it.f > 0 and level[it.v] == -1) {
          level[it.v] = level[u] + 1;
          que.emplace(it.v);
        }
      }
    }
    return level[t] != -1;
  }
  T DFS(int u, T nf) {
    if (u == t) return nf;
    T res = 0;
    while (now[u] < E[u].size()) {
      Edge &it = E[u][now[u]];
      if (it.f > 0 and level[it.v] == level[u] + 1) {
        T tf = DFS(it.v, min(nf, it.f));
        res += tf;
        nf -= tf;
        it.f -= tf;
        E[it.v][it.re].f += tf;
        if (nf == 0) return res;
      } else
        ++now[u];
    }
    if (not res) level[u] = -1;
    return res;
  }
  T flow(T res = 0) {
    while (BFS()) {
      T temp;
      memset(now, 0, sizeof(now));
      while (temp = DFS(s, INF)) {
        res += temp;
        res = min(res, INF);
      }
    }
    return res;
  }
};
const int MAXN = 200;
const int MAXA = int(1e4);
int N;
int A[MAXN];
bool np[MAXA * 2 + 1];
void dfs(int u, const Dinic<int> &din, bool *vis, vector<int> &table) {
  for (int i = 0; i < din.E[u].size(); ++i) {
    int v = din.E[u][i].v;
    if (v == din.s or v == din.t or vis[v]) continue;
    if (A[u] & 1 ^ din.E[u][i].f) continue;
    vis[v] = true;
    table.emplace_back(v);
    dfs(v, din, vis, table);
    return;
  }
}
signed main() {
  ios::sync_with_stdio(0);
  cin >> N;
  for (int i = 0; i < N; ++i) {
    cin >> A[i];
  }
  for (int i = 2; i <= MAXA * 2; ++i) {
    if (np[i]) continue;
    for (int j = i + i; j <= MAXA * 2; j += i) {
      np[j] = true;
    }
  }
  int SOURCE = N, SINK = N + 1;
  Dinic<int> din(N + 2, SOURCE, SINK);
  for (int i = 0; i < N; ++i) {
    if (A[i] & 1) {
      din.add_edge(i, SINK, 2);
    } else {
      din.add_edge(SOURCE, i, 2);
      for (int j = 0; j < N; ++j)
        if (not np[A[i] + A[j]]) {
          din.add_edge(i, j, 1);
        }
    }
  }
  if (din.flow() != N) cout << "Impossible\n", exit(0);
  vector<vector<int> > ans;
  for (int i = 0; i < N; ++i) {
    static bool vis[MAXN];
    if (vis[i]) continue;
    vis[i] = true;
    ans.emplace_back(vector<int>(1, i));
    dfs(i, din, vis, ans.back());
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); ++i) {
    cout << ans[i].size() << " ";
    for (int j = 0; j < ans[i].size(); ++j) {
      cout << ans[i][j] + 1 << " \n"[j + 1 == ans[i].size()];
    }
  }
  return 0;
}