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 long double INF = 1LL << 60, EPS = 1LL >> 60;
int in() {
  char c;
  bool g = false;
  while (c = getchar(), c < '0' || c > '9')
    if (c == '-')
      g = true;
    else
      g = false;
  int x = 0;
  while (c >= '0' && c <= '9') {
    x = x * 10 + c - 48;
    c = getchar();
  }
  return g ? -x : x;
}
void out(int x) {
  int len = 0, data[20];
  while (x) {
    data[len++] = x % 10;
    x /= 10;
  }
  if (!len) data[len++] = 0;
  if (data[0] != abs(data[0])) putchar('-');
  while (len--) putchar(abs(data[len]) + 48);
  putchar('\n');
}
void out(string s) {
  int len = 0;
  while (len++ < s.size()) putchar(s[len - 1]);
  putchar('\n');
}
const int N = 330, M = N * N;
int n, a[N], from[M], to[M], cap[M], cnt;
bool vis[N], prm[100100];
vector<int> al[N], ok[N], vec;
vector<vector<int> > ans;
void add(int v, int u, int c1 = INF, int c2 = 0) {
  from[cnt] = to[cnt + 1] = v;
  from[cnt + 1] = to[cnt] = u;
  cap[cnt] = c1;
  cap[cnt + 1] = c2;
  al[v].push_back(cnt++);
  al[u].push_back(cnt++);
}
int dfs(int v = 0, int mn = 2 * INF) {
  int id, u, x;
  vis[v]++;
  if (v == n + 1) return mn;
  for (int i = 0; i < al[v].size(); i++)
    if (!vis[u = to[id = al[v][i]]] && cap[id] &&
        (x = dfs(u, min(mn, cap[id]))))
      return cap[id] -= x, cap[id ^ 1] += x, x;
  return 0;
}
int flw() {
  int a, mx = 0;
  memset(vis, 0, sizeof(vis));
  while (a = dfs()) mx += a, memset(vis, 0, sizeof(vis));
  return mx;
}
int anss(int v) {
  vis[v] = true;
  vec.push_back(v);
  for (int i = 0; i < ok[v].size(); i++)
    if (!vis[ok[v][i]]) anss(ok[v][i]);
}
int main() {
  for (int i = 2; i < 100100; i++)
    if (!prm[i])
      for (int j = 2 * i; j < 100100; j += i) prm[j]++;
  n = in();
  for (int i = 1; i <= n; i++)
    if ((a[i] = in()) % 2)
      add(0, i, 2, 0);
    else
      add(i, n + 1, 2, 0);
  int k = cnt;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++)
      if ((a[i] % 2) && !prm[a[i] + a[j]]) add(i, j, 1, 0);
  if (flw() - n) return cout << "Impossible" << '\n', 0;
  for (int i = k; i < cnt; i++)
    if (!cap[i] && a[from[i]] % 2)
      ok[from[i]].push_back(to[i]), ok[to[i]].push_back(from[i]);
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i <= n; i++)
    if (!vis[i]) anss(i), ans.push_back(vec), vec.clear();
  cout << ans.size() << '\n';
  for (int i = 0; i < ans.size(); i++) {
    cout << ans[i].size() << " ";
    for (int j = 0; j < ans[i].size(); j++) cout << ans[i][j] << " ";
    cout << '\n';
  }
  return 0;
}