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;
void fast() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
const int INF = 1e9 + 9;
const int N = 210;
const int M = 1e5 + 5;
vector<vector<int>> ans(N);
vector<vector<int>> capacity(N, vector<int>(N, 0));
vector<int> v(N);
vector<bool> p(M, 1);
vector<bool> vis(N, 0);
int n;
int dfs(int a, int flow) {
  if (a == n + 1 || flow == 0) return flow;
  int ans = 0;
  vis[a] = 1;
  for (int i = 0; i <= n + 1; i++) {
    if (vis[i] || capacity[a][i] == 0) continue;
    int temp = dfs(i, min(flow, capacity[a][i]));
    if (temp == 0) continue;
    capacity[a][i] -= temp;
    capacity[i][a] += temp;
    return temp;
  }
  return 0;
}
int get() {
  int ans = 0;
  while (1) {
    int newFlow = dfs(0, INF);
    if (newFlow == 0) break;
    ans += newFlow;
    for (int i = 0; i <= n + 1; i++) vis[i] = 0;
  }
  return ans;
}
void dfs2(int a, int idx) {
  vis[a] = 1;
  ans[idx].push_back(a);
  for (int i = 1; i <= n; i++) {
    if (vis[i]) continue;
    if (v[a] % 2 == 0 && v[i] % 2 == 1 && capacity[a][i] > 0) {
      dfs2(i, idx);
      break;
    }
    if (v[a] % 2 == 1 && v[i] % 2 == 0 && capacity[i][a] > 0) {
      dfs2(i, idx);
      break;
    }
  }
}
void solve() {
  for (int i = 2; i * i < M; i++)
    if (p[i])
      for (int j = i * i; j < M; j += i) p[j] = 0;
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    if (v[i] & 1) {
      cnt++;
      capacity[0][i] = 2;
    } else {
      cnt--;
      capacity[i][n + 1] = 2;
    }
  }
  if (cnt != 0) {
    cout << "Impossible\n";
    return;
  }
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) {
      if (v[i] % 2 == 1 && v[j] % 2 == 0 && p[v[i] + v[j]]) capacity[i][j] = 1;
    }
  int flow = get();
  if (flow != n) {
    cout << "Impossible\n";
    return;
  }
  for (int i = 0; i <= n + 1; i++) vis[i] = 0;
  int idx = 0;
  for (int i = 1; i <= n; i++) {
    if (vis[i]) continue;
    dfs2(i, idx);
    idx++;
  }
  cout << idx << "\n";
  for (int i = 0; i < idx; i++) {
    cout << int(ans[i].size()) << ' ';
    for (int j : ans[i]) cout << j << ' ';
    cout << "\n";
  }
}
int main() {
  fast();
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> v[i];
  solve();
}