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 maxn = 200;
int n;
int a[maxn];
const int maxp = 2e4 + 1;
bool flag[maxp];
struct Edge {
  int from, to, cap, flow;
  Edge(int from, int to, int cap, int flow)
      : from(from), to(to), cap(cap), flow(flow) {}
};
struct Dinic {
  static const int maxn = 202;
  vector<Edge> edges;
  vector<int> G[maxn];
  int n, s, t;
  void add_edge(int from, int to, int cap) {
    edges.push_back(Edge(from, to, cap, 0));
    edges.push_back(Edge(to, from, 0, 0));
    int m = edges.size();
    G[from].push_back(m - 2);
    G[to].push_back(m - 1);
  }
  bool vis[maxn];
  int d[maxn];
  queue<int> q;
  bool bfs() {
    memset(vis, 0, sizeof(vis));
    vis[s] = true;
    d[s] = 0;
    q.push(s);
    while (!q.empty()) {
      int u = q.front();
      q.pop();
      for (int i = 0; i < G[u].size(); i++) {
        Edge &e = edges[G[u][i]];
        if (!vis[e.to] && e.cap > e.flow) {
          vis[e.to] = true;
          d[e.to] = d[u] + 1;
          q.push(e.to);
        }
      }
    }
    return vis[t];
  }
  int cur[maxn];
  int dfs(int u, int a) {
    if (u == t || !a) return a;
    int flow = 0, f;
    for (int &i = cur[u]; i < G[u].size(); i++) {
      Edge &e = edges[G[u][i]];
      if (d[e.to] == d[u] + 1 && (f = dfs(e.to, min(a, e.cap - e.flow)))) {
        flow += f;
        a -= f;
        edges[G[u][i] ^ 0].flow += f;
        edges[G[u][i] ^ 1].flow -= f;
        if (!a) continue;
      }
    }
    return flow;
  }
  int maxFlow(int s, int t, int n) {
    this->s = s;
    this->t = t;
    this->n = n;
    int flow = 0;
    while (bfs()) {
      memset(cur, 0, sizeof(cur));
      flow += dfs(s, INT_MAX);
    }
    return flow;
  }
} solver;
void pre() {
  for (int i = 2; i < maxp; i++) {
    if (flag[i]) continue;
    for (int j = i * 2; j < maxp; j += i) flag[j] = true;
  }
}
bool vis[maxn];
vector<int> G[maxn];
vector<vector<int> > ans;
void dfs(int u) {
  vis[u] = true;
  ans.back().push_back(u);
  for (int i = 0; i < G[u].size(); i++) {
    int v = G[u][i];
    if (vis[v]) continue;
    dfs(v);
  }
}
bool solve() {
  if (n % 2 == 1) return false;
  int cnt[2] = {0, 0};
  for (int i = 0; i < n; i++) cnt[a[i] & 1]++;
  if (cnt[0] != cnt[1]) return false;
  int S = n, T = S + 1, N = T + 1;
  for (int i = 0; i < n; i++) {
    if (a[i] & 1)
      solver.add_edge(S, i, 2);
    else
      solver.add_edge(i, T, 2);
  }
  for (int i = 0; i < n; i++)
    if (a[i] & 1)
      for (int j = 0; j < n; j++)
        if (!flag[a[i] + a[j]]) solver.add_edge(i, j, 1);
  if (solver.maxFlow(S, T, N) != cnt[0] * 2) return false;
  for (int i = 2 * n; i < solver.edges.size(); i += 2) {
    Edge &e = solver.edges[i];
    if (e.flow == 1) {
      G[e.from].push_back(e.to);
      G[e.to].push_back(e.from);
    }
  }
  for (int i = 0; i < n; i++)
    if (!vis[i]) {
      ans.push_back(vector<int>());
      dfs(i);
    }
  for (int i = 0; i < ans.size(); i++)
    for (int j = 0; j < ans[i].size(); j++)
      assert(!flag[a[ans[i][j]] + a[ans[i][(j + 1) % int(ans[i].size())]]]);
  printf("%d\n", ans.size());
  for (int i = 0; i < ans.size(); i++) {
    printf("%d", ans[i].size());
    for (int j = 0; j < ans[i].size(); j++) printf(" %d", ans[i][j] + 1);
    puts("");
  }
  return true;
}
int main() {
  pre();
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  if (!solve()) puts("Impossible");
}