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;
vector<int> leftpartition;
vector<int> rightpartition;
vector<vector<int> > graphflow;
unordered_map<int, bool> primechecker;
vector<vector<int> > graphcap;
vector<vector<int> > graphresid;
vector<int> sourcecap;
vector<int> sinkcap;
bool isPrime(int k) {
  if (primechecker.find(k) != primechecker.end()) return primechecker[k];
  bool primality = true;
  for (int i = 2; i < min(150, k); i++) {
    if (k % i == 0) {
      primality = false;
    }
  }
  primechecker[k] = primality;
  return primality;
}
int bfs(int source, int target) {
  queue<int> toVisit;
  unordered_map<int, int> visited;
  toVisit.push(source);
  visited[source] = -3;
  bool seentarget = false;
  while (!toVisit.empty() && !seentarget) {
    int currentv = toVisit.front();
    toVisit.pop();
    if (currentv == -1) {
      for (int i = 0; i < sourcecap.size(); i++) {
        if (sourcecap[i] != 0) {
          visited[i] = currentv;
          toVisit.push(i);
        }
      }
    } else {
      for (int i = 0; i < graphflow[currentv].size(); i++) {
        int vertexboss = graphflow[currentv][i];
        if (vertexboss == target && sinkcap[currentv % sinkcap.size()] != 0) {
          visited[vertexboss] = currentv;
          seentarget = true;
        } else if (vertexboss != target &&
                   visited.find(vertexboss) == visited.end()) {
          if (graphcap[currentv][vertexboss] != 0) {
            visited[vertexboss] = currentv;
            toVisit.push(vertexboss);
          }
        }
      }
    }
  }
  if (!seentarget) {
    return 0;
  }
  int current = visited[target];
  sinkcap[current % sinkcap.size()] -= 1;
  while (visited[current] != source) {
    graphcap[visited[current]][current] = 0;
    graphcap[current][visited[current]] = 1;
    current = visited[current];
  }
  sourcecap[current] -= 1;
  return 1;
}
int edmondkarp(int source, int target, int currentflow) {
  int pushed = bfs(source, target);
  if (pushed != 0) {
    return edmondkarp(source, target, currentflow + 1);
  }
  return currentflow;
}
int main() {
  int n;
  cin >> n;
  vector<int> foxindexleft;
  vector<int> foxindexright;
  for (int i = 0; i < n; i++) {
    int ai;
    cin >> ai;
    if (ai % 2 == 0) {
      leftpartition.push_back(ai);
      foxindexleft.push_back(i + 1);
    } else {
      rightpartition.push_back(ai);
      foxindexright.push_back(i + 1);
    }
  }
  sourcecap = vector<int>(n / 2, 2);
  sinkcap = vector<int>(n / 2, 2);
  graphcap = vector<vector<int> >(n, vector<int>(n, 0));
  if (leftpartition.size() != rightpartition.size()) {
    cout << "Impossible" << endl;
    return 0;
  }
  graphflow = vector<vector<int> >(n);
  for (int i = 0; i < n / 2; i++) {
    for (int j = 0; j < n / 2; j++) {
      if (isPrime(leftpartition[i] + rightpartition[j])) {
        graphflow[i].push_back((n / 2) + j);
        graphcap[i][(n / 2) + j] = 1;
        graphflow[(n / 2) + j].push_back(i);
      }
    }
  }
  for (int j = 0; j < n / 2; j++) {
    graphflow[(n / 2) + j].push_back(-2);
  }
  int maxflow = edmondkarp(-1, -2, 0);
  if (maxflow < n) {
    cout << "Impossible" << endl;
    return 0;
  }
  vector<vector<int> > newgraph(n);
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (graphcap[j][i] != 0) {
        newgraph[i].push_back(j);
        newgraph[j].push_back(i);
      }
    }
  }
  unordered_set<int> visiteddfs;
  vector<vector<int> > answer;
  for (int i = 0; i < n; i++) {
    vector<int> curpath;
    bool done = (visiteddfs.find(newgraph[i][0]) != visiteddfs.end()) &&
                (visiteddfs.find(newgraph[i][1]) != visiteddfs.end());
    int current = i;
    while (!done) {
      curpath.push_back(current);
      visiteddfs.insert(current);
      bool d1 = (visiteddfs.find(newgraph[current][0]) != visiteddfs.end());
      bool d2 = (visiteddfs.find(newgraph[current][1]) != visiteddfs.end());
      done = d1 && d2;
      if (!d1)
        current = newgraph[current][0];
      else
        current = newgraph[current][1];
    }
    if (curpath.size() != 0) answer.push_back(curpath);
  }
  cout << answer.size() << endl;
  for (int i = 0; i < answer.size(); i++) {
    cout << answer[i].size() << " ";
    for (int j = 0; j < answer[i].size(); j++) {
      if (answer[i][j] < (n / 2)) {
        cout << foxindexleft[answer[i][j]] << " ";
      } else
        cout << foxindexright[answer[i][j] % (n / 2)] << " ";
    }
    cout << endl;
  }
  return 0;
}