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 EPS = 0;
const int INF = 1e9;
const int MAXN = 500;
vector<int> nbrs[MAXN];
int start[MAXN], dist[MAXN];
int res[MAXN][MAXN];
void addEdge(int a, int b, int c) {
  res[a][b] += c;
  nbrs[a].push_back(b);
  nbrs[b].push_back(a);
}
bool bfs(int s, int t, int n) {
  for (int i = 0; i < n; ++i) dist[i] = -1;
  dist[s] = 0;
  queue<int> q;
  q.push(s);
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int v : nbrs[u])
      if (res[u][v] > EPS && dist[v] == -1) {
        dist[v] = dist[u] + 1;
        q.push(v);
      }
  }
  return dist[t] != -1;
}
int dfs(int x, int t, int mini) {
  int ans = 0;
  if (x == t) return mini;
  if (mini <= EPS) return 0;
  for (int& i = start[x]; i < nbrs[x].size(); ++i) {
    int v = nbrs[x][i];
    if (dist[x] + 1 == dist[v] && res[x][v] > EPS) {
      int added = dfs(v, t, min(mini, res[x][v]));
      res[x][v] -= added;
      res[v][x] += added;
      mini -= added;
      ans += added;
      if (mini <= EPS) break;
    }
  }
  return ans;
}
int maxFlow(int s, int t, int n) {
  int res = 0;
  while (bfs(s, t, n)) {
    for (int i = 0; i < n; ++i) start[i] = 0;
    res += dfs(s, t, INF);
  }
  return res;
}
const int MAXP = 20009;
bool composite[MAXP];
void eratostenes() {
  for (int p = 2; p < MAXP; p++) {
    if (!composite[p]) {
      for (int x = 2 * p; x < MAXP; x += p) {
        composite[x] = true;
      }
    }
  }
}
bool isPrime(int x) { return !composite[x]; }
vector<int> resultEdges[MAXN];
int main() {
  eratostenes();
  int n, curId = 0;
  vector<int> odd, even, oddId, evenId;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    if (a % 2 == 0) {
      even.push_back(a);
      evenId.push_back(++curId);
    } else {
      odd.push_back(a);
      oddId.push_back(++curId);
    }
  }
  int evenSize = even.size();
  if (evenSize != odd.size()) {
    cout << "Impossible\n";
    return 0;
  }
  int s = 0, t = 2 * evenSize + 1, graphSize = 2 * evenSize + 2;
  for (int i = 0; i < evenSize; i++) {
    addEdge(s, i + 1, 2);
  }
  for (int i = 0; i < evenSize; i++) {
    for (int j = 0; j < evenSize; j++) {
      if (isPrime(even[i] + odd[j])) {
        addEdge(i + 1, j + evenSize + 1, 1);
      }
    }
  }
  for (int i = 0; i < evenSize; i++) {
    addEdge(i + evenSize + 1, t, 2);
  }
  if (maxFlow(s, t, graphSize) == 2 * evenSize) {
    vector<vector<int> > cycles;
    vector<bool> vis(n + 1);
    for (int i = 0; i < evenSize; i++) {
      for (int j : nbrs[i + 1]) {
        if (res[i + 1][j] == 0) {
          resultEdges[evenId[i]].push_back(oddId[j - evenSize - 1]);
          resultEdges[oddId[j - evenSize - 1]].push_back(evenId[i]);
        }
      }
    }
    for (int i = 1; i <= n; i++) {
      if (!vis[i]) {
        int cur = i;
        cycles.emplace_back();
        vector<int>& vec = cycles.back();
        while (!vis[cur]) {
          vis[cur] = true;
          vec.push_back(cur);
          cur = (vis[resultEdges[cur][0]] ? resultEdges[cur][1]
                                          : resultEdges[cur][0]);
        }
      }
    }
    cout << cycles.size() << '\n';
    for (const auto& cycle : cycles) {
      cout << cycle.size() << ' ';
      for (int x : cycle) {
        cout << x << ' ';
      }
      cout << '\n';
    }
  } else {
    cout << "Impossible\n";
  }
  return 0;
}