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;
string convertstring(long long n) {
  stringstream ss;
  ss << n;
  return ss.str();
}
const int N = 410;
int n;
int a[N];
queue<int> q;
std::vector<int> v[N];
int vis[N];
int par[N];
int g[N][N];
int res[N][N];
std::vector<int> final[N], tmp;
std::vector<int> ans[N];
int src, sink;
int bfs() {
  memset(vis, 0, sizeof(vis));
  memset(par, 0, sizeof(par));
  q.push(src);
  par[src] = -1;
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int nx : v[u]) {
      if (!vis[nx] && g[u][nx] > 0) {
        vis[nx] = 1;
        par[nx] = u;
        q.push(nx);
      }
    }
  }
  return (vis[sink] == 1);
}
int update() {
  int ret = 1000000010;
  int u = sink;
  while (par[u] != -1) {
    ret = min(ret, g[par[u]][u]);
    u = par[u];
  }
  u = sink;
  while (par[u] != -1) {
    g[par[u]][u] -= ret;
    g[u][par[u]] += ret;
    u = par[u];
  }
  return ret;
}
int maxflow() {
  int ans = 0;
  while (bfs()) {
    ans += update();
  }
  return ans;
}
int ok(int x) {
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) return 0;
  }
  return 1;
}
int main() {
  int i, j;
  scanf("%d", &n);
  src = 2 * n + 1;
  sink = 2 * n + 2;
  for (i = (int)0; i < (int)n; i++) {
    scanf("%d", &a[i]);
    if (a[i] % 2) {
      v[src].push_back(i);
      g[src][i] = 2;
    } else {
      v[i].push_back(sink);
      g[i][sink] = 2;
    }
  }
  for (i = (int)0; i < (int)n; i++) {
    for (j = (int)0; j < (int)n; j++) {
      if ((a[i] % 2) && (a[j] % 2 == 0)) {
        if (ok(a[i] + a[j])) {
          v[j].push_back(i);
          v[i].push_back(j);
          res[i][j] = 1;
          g[i][j] = 1;
        }
      }
    }
  }
  if (maxflow() != n) {
    printf("Impossible\n");
    return 0;
  }
  for (i = (int)0; i < (int)n; i++) {
    for (j = (int)0; j < (int)n; j++) {
      if (res[i][j] > 0) {
        if (g[i][j] == 0) {
          ans[i].push_back(j);
          ans[j].push_back(i);
        }
      }
    }
  }
  memset(vis, 0, sizeof(vis));
  int cn = 0;
  for (i = (int)0; i < (int)n; i++) {
    if (!vis[i] && ans[i].size() > 0) {
      int start = ans[i][0];
      tmp.clear();
      tmp.push_back(start);
      tmp.push_back(i);
      tmp.push_back(ans[i][1]);
      vis[start] = 1;
      vis[i] = 1;
      vis[ans[i][1]] = 1;
      int el = ans[i][1];
      while (1) {
        int a = ans[el][0];
        int b = ans[el][1];
        if (vis[a] && vis[b])
          break;
        else if (vis[a]) {
          tmp.push_back(b);
          vis[b] = 1;
          el = b;
        } else if (vis[b]) {
          tmp.push_back(a);
          vis[a] = 1;
          el = a;
        }
      }
      final[cn].push_back(tmp.size());
      for (j = (int)0; j < (int)tmp.size(); j++) final[cn].push_back(tmp[j]);
      cn++;
    }
  }
  cout << cn << "\n";
  for (i = (int)0; i < (int)cn; i++) {
    cout << final[i][0] << " ";
    for (int j = 1; j < final[i].size(); j++) cout << final[i][j] + 1 << " ";
    cout << "\n";
  }
  return 0;
}