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 N = 205, INF = 1e9;
int n, st, en, cnt;
int a[N], c[N][N], f[N][N], pa[N];
vector<int> adj[N], ans[N];
bool used[N];
bool check(int x) {
  int sqr = sqrt(x);
  for (int i = 2; i <= sqr; ++i)
    if (x % i == 0) return false;
  return true;
}
bool bfs() {
  memset(pa, -1, sizeof pa);
  pa[st] = INF;
  queue<int> q;
  q.push(st);
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int i = 0; i <= (int)adj[u].size() - 1; ++i) {
      int v = adj[u][i];
      if (pa[v] == -1 && c[u][v] > f[u][v]) {
        pa[v] = u;
        q.push(v);
      }
    }
  }
  return (pa[en] != -1);
}
void solve() {
  int v = en, u, res = INF;
  while (v != st) {
    u = pa[v];
    res = min(res, c[u][v] - f[u][v]);
    v = u;
  }
  v = en;
  while (v != st) {
    u = pa[v];
    f[u][v] += res;
    f[v][u] -= res;
    v = u;
  }
}
void find(int u) {
  used[u] = true;
  ans[cnt].push_back(u);
  for (int i = 0; i <= (int)adj[u].size() - 1; ++i) {
    int v = adj[u][i];
    if (v != st && v != en && not used[v] && abs(f[u][v]) == 1) {
      find(v);
      return;
    }
  }
}
signed main() {
  cin >> n;
  st = 0;
  en = n + 1;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  for (int i = 1; i <= n; ++i) {
    if (a[i] & 1) {
      adj[st].push_back(i);
      adj[i].push_back(st);
      c[st][i] = 2;
    } else {
      adj[i].push_back(en);
      adj[en].push_back(i);
      c[i][en] = 2;
    }
    for (int j = 1; j <= n; ++j)
      if (check(a[i] + a[j]) && a[i] & 1) {
        adj[i].push_back(j);
        adj[j].push_back(i);
        c[i][j] = 1;
      }
  }
  while (bfs()) solve();
  for (int i = 0; i <= (int)adj[st].size() - 1; ++i) {
    int u = adj[st][i];
    if (f[st][u] != 2) {
      cout << "Impossible";
      return 0;
    }
  }
  for (int i = 0; i <= (int)adj[en].size() - 1; ++i) {
    int u = adj[en][i];
    if (f[u][en] != 2) {
      cout << "Impossible";
      return 0;
    }
  }
  used[st] = used[en] = true;
  for (int i = 1; i <= n; ++i) {
    if (not used[i]) {
      find(i);
      cnt++;
    }
  }
  cout << cnt << "\n";
  for (int i = 0; i <= cnt - 1; ++i) {
    cout << ans[i].size() << " ";
    for (int j = 0; j <= (int)ans[i].size() - 1; ++j) cout << ans[i][j] << ' ';
    cout << "\n";
  }
}