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;
bool ko_no_prime_da(int x) {
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) return false;
  }
  return true;
}
struct edge {
  int to, flow, id;
  edge(int _to, int _flow, int _id) {
    to = _to;
    flow = _flow;
    id = _id;
  }
};
int n, ans;
vector<edge> g[205];
vector<int> ng[205];
vector<int> ansv[70];
bool vis[205];
int dis[205];
int a[205];
set<int> odd, even;
inline void addedge(int from, int to, int flow) {
  edge foo(to, flow, g[to].size()), bar(from, 0, g[from].size());
  g[from].push_back(foo);
  g[to].push_back(bar);
}
int dfs(int x, int cf) {
  if (x == n + 1) return cf;
  for (int i = 0; i < g[x].size(); i++) {
    edge &e = g[x][i];
    if (e.flow != 0 && dis[e.to] > dis[x]) {
      int d = dfs(e.to, min(cf, e.flow));
      if (d) {
        e.flow -= d;
        g[e.to][e.id].flow += d;
        return d;
      }
    }
  }
  return 0;
}
int dinic() {
  int mxf = 0;
  for (;;) {
    queue<int> q;
    q.push(0);
    memset(dis, -1, sizeof(dis));
    dis[0] = 0;
    while (!q.empty()) {
      int x = q.front();
      q.pop();
      for (int i = 0; i < g[x].size(); i++) {
        int y = g[x][i].to;
        if (g[x][i].flow != 0 && dis[y] == -1) {
          dis[y] = dis[x] + 1;
          q.push(y);
        }
      }
    }
    if (dis[n + 1] == -1) {
      return mxf;
    }
    mxf += dfs(0, 0x3f3f3f3f);
  }
}
void ngdfs(int x) {
  vis[x] = true;
  ansv[ans].push_back(x);
  for (int i = 0; i < ng[x].size(); i++) {
    int y = ng[x][i];
    if (!vis[y]) {
      ngdfs(y);
    }
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] & 1) {
      odd.insert(i);
      addedge(0, i, 2);
    } else {
      even.insert(i);
      addedge(i, n + 1, 2);
    }
  }
  for (set<int>::iterator i = odd.begin(); i != odd.end(); i++) {
    for (set<int>::iterator j = even.begin(); j != even.end(); j++) {
      if (ko_no_prime_da(a[*i] + a[*j])) {
        addedge(*i, *j, 1);
      }
    }
  }
  int mxf = dinic();
  cerr << "MXF: " << mxf << endl;
  if (mxf != 2 * even.size()) {
    cout << "Impossible" << endl;
    return 0;
  }
  for (int x = 1; x <= n; x++) {
    if (!(a[x] & 1)) continue;
    for (int i = 0; i < g[x].size(); i++) {
      int y = g[x][i].to, flow = g[x][i].flow;
      if (flow == 0) {
        ng[x].push_back(y);
        ng[y].push_back(x);
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    if (!vis[i]) {
      ++ans;
      ngdfs(i);
    }
  }
  cout << ans << endl;
  for (int i = 1; i <= ans; i++) {
    cout << ansv[i].size() << ' ';
    for (int j = 0; j < ansv[i].size(); j++) {
      cout << ansv[i][j] << ' ';
    }
    cout << endl;
  }
  return 0;
}