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 N = (int)2e2 + 77;
const int inf = (int)1e9 + 77;
const int INF = 1000000000;
struct Edge {
  int a, b, cap, flow;
};
struct MaxFlow {
  int n, s, t;
  vector<int> d, ptr, q;
  vector<Edge> e;
  vector<vector<int>> g;
  int i, j;
  MaxFlow(int n) : n(n), d(n), ptr(n), q(n), g(n) {
    e.clear();
    for (int i = 0; i < n; i++) {
      g[i].clear();
      ptr[i] = 0;
    }
  }
  void addEdge(int a, int b, int cap) {
    Edge e1 = {a, b, cap, 0};
    Edge e2 = {b, a, 0, 0};
    g[a].push_back((int)e.size());
    e.push_back(e1);
    g[b].push_back((int)e.size());
    e.push_back(e2);
  }
  int getMaxFlow(int _s, int _t) {
    s = _s;
    t = _t;
    int flow = 0;
    for (;;) {
      if (!bfs()) break;
      for (int i = 0; i < n; i++) ptr[i] = 0;
      while (int pushed = dfs(s, INF)) flow += pushed;
    }
    return flow;
  }
  void trace(int u, vector<int> &v, int vis[], int a[]) {
    if (vis[u]) return;
    if (u <= n - 20) v.push_back(u);
    vis[u] = 1;
    for (int i = 0; i < g[u].size(); i++) {
      int id = g[u][i];
      int to = e[id].b;
      int flow = a[u] % 2 == 0 ? e[id].cap - e[id].flow : e[id].flow;
      if (flow > 0) trace(to, v, vis, a);
    }
  }

 private:
  bool bfs() {
    int qh = 0, qt = 0;
    q[qt++] = s;
    for (int i = 0; i < n; i++) d[i] = -1;
    d[s] = 0;
    while (qh < qt && d[t] == -1) {
      int v = q[qh++];
      for (int i = 0; i < g[v].size(); i++) {
        int id = g[v][i], to = e[id].b;
        if (d[to] == -1 && e[id].flow < e[id].cap) {
          q[qt++] = to;
          d[to] = d[v] + 1;
        }
      }
    }
    return d[t] != -1;
  }
  int dfs(int v, int flow) {
    if (!flow) return 0;
    if (v == t) return flow;
    for (; ptr[v] < (int)g[v].size(); ++ptr[v]) {
      int id = g[v][ptr[v]], to = e[id].b;
      if (d[to] != d[v] + 1) continue;
      int pushed = dfs(to, min(flow, e[id].cap - e[id].flow));
      if (pushed) {
        e[id].flow += pushed;
        e[id ^ 1].flow -= pushed;
        return pushed;
      }
    }
    return 0;
  }
};
int main() {
  int n, odd = 0, a[N], p[1000 * 100] = {0};
  for (int i = 2; i < 1000 * 100; i++) {
    if (p[i]) continue;
    for (int j = i + i; j < 1000 * 100; j += i) p[j] = 1;
  }
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] & 1) ++odd;
  }
  if (2 * odd != n) {
    puts("Impossible");
    return 0;
  }
  MaxFlow flow(n + 20);
  for (int i = 1; i <= n; i++) {
    if (a[i] & 1)
      for (int j = 1; j <= n; j++)
        if (p[a[i] + a[j]] == 0) {
          flow.addEdge(i, j, 1);
        }
    if (a[i] & 1)
      flow.addEdge(n + 1, i, 2);
    else
      flow.addEdge(i, n + 2, 2);
  }
  int f = flow.getMaxFlow(n + 1, n + 2);
  if (f != 2 * odd) {
    puts("Impossible");
    return 0;
  }
  int vis[N] = {0};
  vector<int> v;
  vector<vector<int>> ans;
  for (int i = 1; i <= n; i++) {
    if (vis[i] == 0 and a[i] % 2 == 0) {
      v.clear();
      flow.trace(i, v, vis, a);
      ans.push_back(v);
    }
  }
  cout << ans.size() << endl;
  for (auto table : ans) {
    cout << table.size() << " ";
    for (auto age : table) cout << age << " ";
    cout << endl;
  }
  return 0;
}