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>
bool debug = 0;
const double PI = acos(-1.0);
const double eps = 1e-9;
using namespace std;
const int MAXN = 500;
const int INF = 1000000000;
struct edge {
  int a, b, cap, flow;
};
int sz, s, t, d[MAXN], ptr[MAXN], q[MAXN];
vector<edge> e;
vector<int> g[MAXN];
void add_edge(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);
}
bool bfs() {
  int qh = 0, qt = 0;
  q[qt++] = s;
  memset(d, -1, sz * sizeof d[0]);
  d[s] = 0;
  while (qh < qt && d[t] == -1) {
    int v = q[qh++];
    for (size_t 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 dinic() {
  int flow = 0;
  for (;;) {
    if (!bfs()) break;
    memset(ptr, 0, sz * sizeof ptr[0]);
    while (int pushed = dfs(s, INF)) flow += pushed;
  }
  return flow;
}
set<int> prime;
bool aux[30000];
void sieve() {
  for (int i = 2; i < 30000; i++) {
    if (aux[i] == 0) {
      prime.insert(i);
      for (int j = i; j < 30000; j += i) {
        aux[j] = 1;
      }
    }
  }
}
vector<int> res[500];
vector<pair<int, int> > odd, even;
bool vis[500];
int cnt;
vector<int> adj[500];
vector<int> gr[500];
void dfs(int x) {
  vis[x] = 1;
  if (debug)
    cout << "x"
         << " = " << (x) << endl;
  res[cnt].push_back(x);
  for (int p : gr[x]) {
    if (vis[p] == 0) {
      dfs(p);
    }
  }
}
int main() {
  int n;
  sieve();
  cin >> n;
  int x;
  for (int i = 0; i < n; i++) {
    cin >> x;
    if (x % 2 == 0) {
      even.push_back({x, i + 1});
    } else
      odd.push_back({x, i + 1});
  }
  if (even.size() != odd.size()) {
    cout << "Impossible" << endl;
    return 0;
  }
  s = 0;
  t = n + 2;
  sz = n + 20;
  for (pair<int, int> j : odd) {
    add_edge(s, j.second, 2);
  }
  for (pair<int, int> j : even) {
    add_edge(j.second, t, 2);
  }
  for (pair<int, int> i : odd) {
    for (pair<int, int> j : even) {
      if (prime.find(i.first + j.first) != prime.end()) {
        adj[i.second].push_back(e.size());
        add_edge(i.second, j.second, 1);
      }
    }
  }
  int aux = dinic();
  if (aux != 2 * even.size()) {
    cout << "Impossible" << endl;
    if (n == 200) printf("%d\n", aux);
    return 0;
  }
  for (pair<int, int> i : odd) {
    for (int p : adj[i.second]) {
      if (e[p].flow == 1) {
        gr[i.second].push_back(e[p].b);
        gr[e[p].b].push_back(i.second);
      }
    }
  }
  for (pair<int, int> i : odd) {
    if (vis[i.second] == 0) {
      cnt++;
      dfs(i.second);
      if (debug) cout << endl;
    }
  }
  cout << cnt << endl;
  for (int i = 1; i <= cnt; i++) {
    printf("%d ", (int)res[i].size());
    for (int j : res[i]) {
      printf("%d ", j);
    }
    cout << endl;
  }
  cout << endl;
  return 0;
}