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 mod = 1e9 + 7;
struct edge {
  int a, b, cap, flow;
};
int n;
vector<edge> e;
vector<vector<int> > g, gr;
vector<int> level, ptr, comp;
vector<char> used;
vector<vector<int> > ans;
void dfs2(int v) {
  used[v] = 1;
  comp.push_back(v);
  for (int i = 0; i < gr[v].size(); i++) {
    int to = gr[v][i];
    if (!used[to]) dfs2(to);
  }
}
void add_edge(int v, int to, int cap) {
  edge a = {v, to, cap, 0};
  edge b = {to, v, 0, 0};
  g[v].push_back(e.size());
  e.push_back(a);
  g[to].push_back(e.size());
  e.push_back(b);
}
bool bfs() {
  queue<int> q;
  level.assign(n + 15, -1);
  q.push(n + 10);
  level[n + 10] = 0;
  while (!q.empty()) {
    int v = q.front();
    q.pop();
    if (v == n + 11) {
      return true;
    }
    for (int i = 0; i < g[v].size(); i++) {
      int ind = g[v][i];
      int to = e[ind].b;
      if (e[ind].cap > e[ind].flow && level[to] == -1) {
        level[to] = level[v] + 1;
        q.push(to);
      }
    }
  }
  return false;
}
int dfs(int v, int flow) {
  if (v == n + 11) return flow;
  if (flow == 0) return 0;
  for (int i = ptr[v]; i < g[v].size(); i++, ptr[v]++) {
    int ind = g[v][i];
    int to = e[ind].b;
    if (level[to] != level[v] + 1) {
      continue;
    }
    int add = dfs(to, min(flow, e[ind].cap - e[ind].flow));
    if (add) {
      e[ind].flow += add;
      e[ind ^ 1].flow -= add;
      return add;
    }
  }
  return 0;
}
int find() {
  int flow = 0;
  while (bfs()) {
    ptr.assign(n + 15, 0);
    while (int add = dfs(n + 10, 1e9)) flow += add;
  }
  return flow;
}
int main() {
  cin >> n;
  g.resize(n + 15);
  vector<int> arr(n);
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  vector<char> pr(1e5, true);
  pr[0] = pr[1] = 0;
  for (int i = 2; i < pr.size(); i++) {
    if (pr[i]) {
      for (int j = i + i; j < pr.size(); j += i) pr[j] = 0;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      int numb = arr[i] + arr[j];
      if (pr[numb]) {
        if (arr[i] % 2 == 1) {
          add_edge(j, i, 1);
        } else {
          add_edge(i, j, 1);
        }
      }
    }
  }
  for (int i = 0; i < n; i++) {
    if (arr[i] % 2 == 1) {
      add_edge(i, n + 11, 2);
    } else {
      add_edge(n + 10, i, 2);
    }
  }
  int res = find();
  if (res != n) {
    cout << "Impossible";
    return 0;
  }
  gr.resize(n);
  for (int i = 0; i < e.size(); i++) {
    int v = e[i].a, to = e[i].b;
    int flow = e[i].flow;
    if (v <= n && to <= n && flow) {
      gr[v].push_back(to);
      gr[to].push_back(v);
    }
  }
  used.assign(g.size(), false);
  for (int i = 0; i < gr.size(); i++) {
    if (!used[i]) {
      comp.clear();
      dfs2(i);
      ans.push_back(comp);
    }
  }
  cout << ans.size() << "\n";
  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 << " ";
    }
    cout << "\n";
  }
  return 0;
}