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 INF = 1 << 30;
struct Dinic {
  struct Edge {
    int to, flow;
    Edge(int a, int b) : to(a), flow(b) {}
  };
  vector<vector<int>> G;
  vector<int> dis;
  vector<Edge> e;
  int n, s, t;
  Dinic(int sz) : n(sz), G(sz + 1), dis(sz + 1) {}
  void add(int u, int v, int f) {
    G[u].emplace_back(e.size());
    e.emplace_back(v, f);
    G[v].emplace_back(e.size());
    e.emplace_back(u, 0);
  }
  bool bfs() {
    fill(begin(dis), end(dis), -1);
    queue<int> que;
    que.emplace(s);
    dis[s] = 0;
    while (que.size()) {
      int x = que.front();
      que.pop();
      for (int id : G[x]) {
        int y = e[id].to;
        if (e[id].flow > 0 && dis[y] == -1) {
          dis[y] = dis[x] + 1;
          que.emplace(y);
        }
      }
    }
    return dis[t] != -1;
  }
  int dfs(int x, int f = INF) {
    if (x == t || f == 0) return f;
    int a, flow = 0;
    for (int id : G[x]) {
      int y = e[id].to;
      if (e[id].flow > 0 && dis[y] == dis[x] + 1) {
        a = dfs(y, min(f, e[id].flow));
        e[id ^ 1].flow += a;
        e[id].flow -= a;
        flow += a;
        f -= a;
        if (!f) return flow;
      }
    }
    return flow;
  }
  int solve(int _s, int _t) {
    s = _s;
    t = _t;
    int df, flow = 0;
    while (bfs()) {
      while (df = dfs(s)) flow += df;
    }
    return flow;
  }
};
vector<bool> isprime(int sz) {
  vector<bool> ret(sz + 1, true);
  ret[0] = ret[1] = false;
  for (int i = 2; i <= sz; i++) {
    if (ret[i]) {
      for (int j = i + i; j <= sz; j += i) {
        ret[j] = false;
      }
    }
  }
  return ret;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int N;
  cin >> N;
  if (N & 1) {
    cout << "Impossible\n";
    return 0;
  }
  vector<int> arr(N + 1);
  auto is = isprime(20000);
  for (int i = 1; i <= N; i++) {
    cin >> arr[i];
  }
  Dinic loli(N + 1);
  for (int i = 1; i <= N; i++) {
    if (arr[i] & 1) {
      loli.add(0, i, 2);
    } else {
      loli.add(i, N + 1, 2);
    }
    for (int j = 1; j <= N; j++) {
      if (is[arr[i] + arr[j]]) {
        if (arr[i] % 2 == 1 && arr[j] % 2 == 0) loli.add(i, j, 1);
      }
    }
  }
  if (loli.solve(0, N + 1) != N) {
    cout << "Impossible\n";
    return 0;
  }
  vector<vector<int>> G(N + 1);
  for (int i = 1; i <= N; i++) {
    for (int id : loli.G[i]) {
      if (arr[i] % 2 == 1 && loli.e[id].flow == 0) {
        G[i].push_back(loli.e[id].to);
        G[loli.e[id].to].push_back(i);
      }
    }
  }
  vector<vector<int>> ans;
  vector<bool> vis(N + 1);
  vector<int> stk;
  function<void(int)> dfs = [&](int x) {
    vis[x] = true;
    stk.push_back(x);
    for (int y : G[x]) {
      if (!vis[y]) dfs(y);
    }
  };
  for (int i = 1; i <= N; i++) {
    if (!vis[i]) {
      stk.clear();
      dfs(i);
      ans.push_back(stk);
    }
  }
  cout << ans.size() << '\n';
  for (auto it : ans) {
    cout << it.size();
    for (int x : it) {
      cout << ' ' << x;
    }
    cout << '\n';
  }
  return 0;
}