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 INF = 1000000000;
const int MAXN = 210;
const int MAXA = 2 * 10000 + 10;
const int MAXE = MAXN * MAXN * 2;
int cap[MAXE], aft[MAXE], to[MAXE], head[MAXN];
bool marked[MAXN];
bool nprime[MAXA + 10];
vector<int> pth, edges[MAXN];
vector<vector<int> > paths;
int a[MAXN];
int ecnt = 0;
void connect(int a, int b, int w) {
  aft[ecnt] = head[a];
  head[a] = ecnt;
  to[ecnt] = b;
  cap[ecnt] = w;
  ecnt++;
  aft[ecnt] = head[b];
  head[b] = ecnt;
  to[ecnt] = a;
  cap[ecnt] = 0;
  ecnt++;
}
int dfs(int v, int d, int c) {
  if (v == d) return c;
  marked[v] = true;
  for (int i = head[v]; i != -1; i = aft[i])
    if (!marked[to[i]] && cap[i] > 0) {
      int w = dfs(to[i], d, min(c, cap[i]));
      if (w > 0) {
        cap[i] -= w;
        cap[i ^ 1] += w;
        return w;
      }
    }
  return 0;
}
int maxFlow(int source, int sink) {
  int ans = 0;
  int x;
  do {
    memset(marked, false, sizeof marked);
    x = dfs(source, sink, INF);
    ans += x;
  } while (x);
  return ans;
}
void fp(int v) {
  pth.push_back(v);
  marked[v] = true;
  for (int i = 0; i < edges[v].size(); i++) {
    int u = edges[v][i];
    if (!marked[u]) fp(u);
  }
}
int main() {
  int n;
  cin >> n;
  int source = n, sink = n + 1;
  head[source] = head[sink] = -1;
  for (int i = 0; i < n; i++) {
    head[i] = -1;
    cin >> a[i];
    if (a[i] % 2 == 0)
      connect(source, i, 2);
    else
      connect(i, sink, 2);
  }
  nprime[0] = nprime[1] = true;
  for (int i = 2; i <= MAXA; i++)
    if (!nprime[i])
      for (int j = 2 * i; j <= MAXA; j += i) nprime[j] = true;
  for (int i = 0; i < n; i++)
    if (a[i] % 2 == 0)
      for (int j = 0; j < n; j++)
        if (!nprime[a[i] + a[j]]) connect(i, j, 1);
  if (maxFlow(source, sink) == n) {
    for (int i = 0; i < n; i++)
      if (a[i] % 2 == 0) {
        for (int j = head[i]; j != -1; j = aft[j])
          if (to[j] < n && cap[j] == 0) {
            edges[i].push_back(to[j]);
            edges[to[j]].push_back(i);
          }
      }
    memset(marked, false, sizeof marked);
    for (int i = 0; i < n; i++)
      if (!marked[i]) {
        pth.clear();
        fp(i);
        paths.push_back(pth);
      }
    cout << paths.size() << "\n";
    for (int i = 0; i < paths.size(); i++) {
      cout << paths[i].size() << " ";
      for (int j = 0; j < paths[i].size(); j++) cout << paths[i][j] + 1 << " ";
      cout << "\n";
    }
  } else
    cout << "Impossible" << endl;
}