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>
const int N = 220;
const int Q = 100100;
using namespace std;
struct edge {
  int a, b, c, flow;
};
const int MAXN = 200200;
const int inf_int = 1e9;
struct Flow {
  vector<int> g[MAXN];
  vector<edge> e;
  inline int add_edge(int a, int b, int c) {
    edge e1 = {a, b, c, 0};
    edge e2 = {b, a, 0, 0};
    int id = e.size();
    g[a].push_back(id);
    e.push_back(e1);
    g[b].push_back(id + 1);
    e.push_back(e2);
    return id;
  }
  int s, t, n;
  int ptr[MAXN], dis[MAXN], q[MAXN];
  void init(int S, int T, int N) {
    s = S;
    t = T;
    n = N;
  }
  bool bfs() {
    fill(dis, dis + n, inf_int);
    dis[s] = 0;
    int qh = 0, qt = 1;
    q[0] = s;
    while (qh < qt) {
      int v = q[qh++];
      for (int id : g[v]) {
        edge &r = e[id];
        int to = r.b;
        if (r.c > r.flow && dis[to] > dis[v] + 1) {
          dis[to] = dis[v] + 1;
          q[qt++] = to;
        }
      }
    }
    return dis[t] != inf_int;
  }
  int dfs(int v, int flow) {
    if (v == t) return flow;
    for (; ptr[v] < g[v].size(); ++ptr[v]) {
      int id = g[v][ptr[v]];
      edge &r = e[id];
      if (r.c > r.flow && dis[r.b] == dis[v] + 1) {
        int pushed = dfs(r.b, min(flow, r.c - r.flow));
        if (pushed) {
          e[id].flow += pushed;
          e[id ^ 1].flow -= pushed;
          return pushed;
        }
      }
    }
    return 0;
  }
  void delete_all() {
    e.clear();
    for (int i = 0; i < n; ++i) {
      g[i].clear();
    }
  }
  void clear() {
    int m = e.size();
    for (int i = 0; i < m; ++i) {
      e[i].flow = 0;
    }
  }
  int flow() {
    int res = 0;
    while (bfs()) {
      fill(ptr, ptr + n, 0);
      while (int pushed = dfs(s, inf_int)) {
        res += pushed;
      }
    }
    return res;
  }
} flow;
int n;
int a[N];
int used[Q];
int id[N][N];
vector<int> v[N];
int main() {
  ios_base::sync_with_stdio(false);
  for (int i = 2; i < Q; i++)
    if (!used[i]) {
      for (int j = i + i; j < Q; j += i) {
        used[j] = 1;
      }
    }
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  int A = 0, B = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      if (used[a[i] + a[j]] == 0) {
        if (a[i] & 1) {
          id[i][j] = flow.add_edge(i, j, 1);
        } else {
          id[i][j] = flow.add_edge(j, i, 1);
        }
      }
    }
    if (a[i] & 1) {
      A += 1;
      flow.add_edge(0, i, 2);
    } else {
      B += 1;
      flow.add_edge(i, n + 1, 2);
    }
  }
  flow.init(0, n + 1, n + 2);
  if (A != B || flow.flow() != A * 2) {
    cout << "Impossible"
         << "\n";
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++)
      if (!used[a[i] + a[j]]) {
        if (flow.e[id[i][j]].flow == 1) {
          v[i].push_back(j);
          v[j].push_back(i);
        }
      }
  }
  vector<int> used(n + 1, 0);
  vector<vector<int> > res;
  for (int i = 1; i <= n; i++)
    if (!used[i]) {
      int x = i;
      res.push_back({});
      while (!used[x]) {
        used[x] = 1;
        res.back().push_back(x);
        for (int y : v[x]) {
          if (!used[y]) {
            x = y;
            break;
          }
        }
      }
    }
  cout << res.size() << "\n";
  for (auto p : res) {
    cout << p.size() << " ";
    for (int x : p) cout << x << " ";
    cout << "\n";
  }
}