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 = 1e9 + 7;
const int N = 205;
const int M = 2e4 + 2;
vector<int> adj[N];
struct Dinic {
  int n, s, t;
  struct Edge {
    int to, cap, flow, rev;
    Edge(int to = 0, int cap = 0, int flow = 0, int rev = 0)
        : to(to), cap(cap), flow(flow), rev(rev) {}
  };
  vector<int> d;
  vector<int> ptr;
  vector<vector<Edge>> g;
  Dinic(int n = 0, int s = 0, int t = 0)
      : n(n), s(s), t(t), d(n + 2), ptr(n + 2), g(n + 2) {}
  void addEdge(int u, int v, int cap) {
    g[u].emplace_back(v, cap, 0, g[v].size());
    g[v].emplace_back(u, 0, 0, g[u].size() - 1);
  }
  bool bfs() {
    fill(d.begin(), d.end(), -1);
    fill(ptr.begin(), ptr.end(), 0);
    queue<int> q;
    d[s] = 0;
    q.push(s);
    while (!q.empty()) {
      int u = q.front();
      q.pop();
      for (auto e : g[u]) {
        if (d[e.to] == -1 && e.cap > e.flow) {
          d[e.to] = d[u] + 1;
          q.push(e.to);
        }
      }
    }
    return d[t] != -1;
  }
  int dfs(int u, int flow) {
    if (u == t) {
      return flow;
    }
    for (int &i = ptr[u]; i < (int)g[u].size(); i++) {
      auto &e = g[u][i];
      if (e.cap <= e.flow || d[e.to] != d[u] + 1) continue;
      int nxt = dfs(e.to, min(flow, e.cap - e.flow));
      if (nxt) {
        e.flow += nxt;
        g[e.to][e.rev].flow -= nxt;
        return nxt;
      }
    }
    return 0;
  }
  int maxFlow() {
    int ans = 0;
    while (bfs()) {
      while (true) {
        int now = dfs(s, inf);
        if (now)
          ans += now;
        else
          break;
      }
    }
    return ans;
  }
  void trace() {
    for (int i = 1; i <= n - 2; i++) {
      for (int j = 0; j < g[i].size(); j++) {
        if (g[i][j].flow == 1 && g[i][j].cap != 0) {
          adj[i].push_back(g[i][j].to);
          adj[g[i][j].to].push_back(i);
        }
      }
    }
  }
};
int ar[N], wow = 0;
bool check[M], used[N];
vector<int> lis[N];
void dfs1(int x) {
  for (int i = 0; i < adj[x].size(); i++) {
    if (!used[adj[x][i]]) {
      used[adj[x][i]] = true;
      lis[wow].push_back(adj[x][i]);
      dfs1(adj[x][i]);
    }
  }
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, i, j, k, l = 0, z = 0;
  cin >> n;
  if ((n & 1)) {
    cout << "Impossible";
    return 0;
  }
  for (i = 1; i <= n; i++) {
    cin >> ar[i];
    if ((ar[i] & 1)) {
      l++;
    } else {
      z++;
    }
  }
  if (l != z) {
    cout << "Impossible";
    return 0;
  }
  check[1] = true;
  for (i = 1; i <= 2e4; i++) {
    if (!check[i]) {
      for (j = i * i; j <= 2e4; j += i) {
        check[j] = true;
      }
    }
  }
  Dinic dn(n + 2, n + 1, n + 2);
  for (i = 1; i <= n; i++) {
    if ((ar[i] & 1)) {
      dn.addEdge(n + 1, i, 2);
      for (j = 1; j <= n; j++) {
        if (!check[ar[i] + ar[j]]) {
          dn.addEdge(i, j, 1);
        }
      }
    } else {
      dn.addEdge(i, n + 2, 2);
    }
  }
  if (dn.maxFlow() != n) {
    cout << "Impossible";
    return 0;
  }
  dn.trace();
  for (i = 1; i <= n; i++) {
    if (!used[i]) {
      used[i] = true;
      wow++;
      lis[wow].push_back(i);
      dfs1(i);
    }
  }
  cout << wow << '\n';
  for (i = 1; i <= wow; i++) {
    cout << lis[i].size() << ' ';
    for (j = 0; j < lis[i].size(); j++) {
      cout << lis[i][j] << ' ';
    }
    cout << '\n';
  }
}