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 = 1e6, inf = 1e7;
int isPrime[N + 2];
vector<int> prime;
void seive(int n) {
  prime.push_back(2);
  isPrime[1] = 1;
  for (int i = 4; i <= n; i += 2) isPrime[i] = 1;
  int sq = sqrt(n + 1);
  for (int i = 3; i <= n; i += 2) {
    if (isPrime[i]) continue;
    prime.push_back(i);
    if (i > sq) continue;
    for (int j = i * i; j <= n; j += 2 * i) isPrime[j] = 1;
  }
}
struct edge {
  int a, b, f, c;
};
int sr, sn;
vector<edge> ed;
vector<int> adj[N + 2];
void clear(void) {
  ed.clear();
  for (int i = 0; i <= sn; i++) adj[i].clear();
}
void addEdge(int a, int b, int c) {
  edge e;
  e = {a, b, 0, c};
  adj[a].push_back(ed.size());
  ed.push_back(e);
  e = {b, a, 0, 0};
  adj[b].push_back(ed.size());
  ed.push_back(e);
}
int dis[N + 2], pt[N + 2];
bool bfs(void) {
  for (int i = 0; i <= sn; i++) dis[i] = inf;
  queue<int> q;
  q.push(sr);
  dis[sr] = 0;
  while (q.size()) {
    int u = q.front();
    q.pop();
    for (auto x : adj[u]) {
      int v = ed[x].b;
      if (dis[v] == inf && ed[x].f < ed[x].c) dis[v] = dis[u] + 1, q.push(v);
    }
  }
  return dis[sn] != inf;
}
int dfs(int u, int flow) {
  if (!flow || u == sn) return flow;
  for (; pt[u] < adj[u].size(); pt[u]++) {
    int id = adj[u][pt[u]];
    int v = ed[id].b;
    if (dis[v] != dis[u] + 1) continue;
    if (int pushed = dfs(v, min(flow, ed[id].c - ed[id].f))) {
      ed[id].f += pushed;
      ed[id ^ 1].f -= pushed;
      return pushed;
    }
  }
  return 0;
}
int dinic(void) {
  int flow = 0;
  while (bfs()) {
    for (int i = 0; i <= sn; i++) pt[i] = 0;
    while (int pushed = dfs(sr, inf)) flow += pushed;
  }
  return flow;
}
int aa[N + 2], vis[N + 2];
vector<int> ad[N + 2], cir;
void dfs(int node) {
  vis[node] = 1;
  cir.push_back(node);
  for (auto x : ad[node])
    if (!vis[x]) dfs(x);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  seive(100000);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> aa[i];
  sr = 0, sn = n + 1;
  for (int i = 1; i <= n; i++) {
    if (aa[i] % 2 == 0)
      addEdge(sr, i, 2);
    else
      addEdge(i, sn, 2);
  }
  for (int i = 1; i <= n; i++) {
    if (aa[i] % 2) continue;
    for (int j = 1; j <= n; j++)
      if (aa[j] % 2 && !isPrime[aa[i] + aa[j]]) addEdge(i, j, 1);
  }
  if (dinic() != n) cout << "Impossible\n", exit(0);
  for (auto x : ed) {
    if (x.f != 1) continue;
    ad[x.a].push_back(x.b);
    ad[x.b].push_back(x.a);
  }
  vector<vector<int> > ans;
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i <= n; i++) {
    if (vis[i]) continue;
    cir.clear();
    dfs(i);
    ans.push_back(cir);
  }
  cout << ans.size() << endl;
  for (auto x : ans) {
    cout << x.size();
    for (auto z : x) cout << " " << z;
    cout << endl;
  }
  return 0;
}