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;
set<int> edges[1205];
map<pair<int, int>, int> leng;
int SOURCE = 0;
int SINK = 1200;
int odd[205];
int oindex[205];
int even[205];
int eindex[205];
int vis[1205];
int visit[605];
vector<int> mapit[605];
int oddc = 1, evenc = 1;
vector<int> path;
int flow = 0;
int push_flow(int node) {
  vis[node] = 1;
  if (node == SINK) {
    path.push_back(SINK);
    return 1e9;
  }
  for (set<int>::iterator g = edges[node].begin(); g != edges[node].end();
       g++) {
    if (vis[*g]) continue;
    int r = leng[pair<int, int>(node, *g)];
    if (r == 0) continue;
    int k = push_flow(*g);
    if (k == -1) continue;
    path.push_back(node);
    return min(k, r);
  }
  return -1;
}
void ford() {
  while (true) {
    memset(vis, 0, sizeof(vis));
    path.clear();
    int k = push_flow(SOURCE);
    if (k == -1) break;
    flow += k;
    for (int g = 0; g + 1 < path.size(); g++) {
      leng[pair<int, int>(path[g], path[g + 1])] += k;
      edges[path[g]].insert(path[g + 1]);
      leng[pair<int, int>(path[g + 1], path[g])] -= k;
      if (leng[pair<int, int>(path[g + 1], path[g])] == 0)
        edges[path[g + 1]].erase(path[g]);
    }
  }
}
bool checkprime(int num) {
  for (int g = 2; g * g <= num; g++) {
    if (num % g == 0) return false;
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(0);
  int N;
  cin >> N;
  int odder = 0, evener = 0;
  for (int g = 0; g < N; g++) {
    int T;
    cin >> T;
    if (T & 1) {
      oindex[oddc] = g + 1;
      odd[oddc++] = T;
      odder++;
    } else {
      eindex[evenc] = g + 1;
      even[evenc++] = T;
      evener++;
    }
  }
  if (odder != evener) {
    cout << "Impossible";
    return 0;
  }
  for (int g = 1; g < oddc; g++) {
    edges[SOURCE].insert(g);
    leng[pair<int, int>(SOURCE, g)] += 2;
  }
  for (int g = 1; g < oddc; g++) {
    for (int y = 1; y < evenc; y++) {
      if (checkprime(odd[g] + even[y])) {
        edges[g].insert(300 + y);
        leng[pair<int, int>(g, 300 + y)] = 1;
      }
    }
  }
  for (int g = 1; g < evenc; g++) {
    edges[300 + g].insert(SINK);
    leng[pair<int, int>(300 + g, SINK)] = 2;
  }
  ford();
  if (flow == 2 * (oddc - 1)) {
    for (int g = 1; g < oddc; g++) {
      for (int y = 1; y < evenc; y++) {
        if (leng[pair<int, int>(300 + y, g)]) {
          mapit[300 + y].push_back(g);
          mapit[g].push_back(300 + y);
        }
      }
    }
    vector<vector<int> > tooutput;
    int answer = 0;
    for (int g = 1; g < oddc; g++) {
      if (visit[g]) continue;
      vector<int> ans;
      int first = g;
      while (true) {
        ans.push_back(first);
        int x = visit[mapit[first][0]];
        int y = visit[mapit[first][1]];
        visit[first] = 1;
        if (x + y == 2) break;
        if (x)
          first = mapit[first][1];
        else
          first = mapit[first][0];
      }
      tooutput.push_back(ans);
    }
    cout << tooutput.size() << '\n';
    for (int g = 0; g < tooutput.size(); g++) {
      cout << tooutput[g].size() << ' ';
      for (int y = 0; y < tooutput[g].size(); y++) {
        if (tooutput[g][y] > 300) {
          cout << eindex[tooutput[g][y] - 300] << ' ';
        } else
          cout << oindex[tooutput[g][y]] << ' ';
      }
      cout << '\n';
    }
    return 0;
  }
  cout << "Impossible";
  return 0;
}