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, M = 40005;
struct edge {
  int to, next, f;
} e[M];
int head[N], tot = 1, sum;
int dis[N], q[N], n, top;
int fl[M], a[N], SS[2];
int id[N][N], vis[N], S, T;
vector<int> vec[N];
vector<int> ans[N];
void init() {
  for (int i = (int)(2); i <= (int)((M - 1)); i++)
    for (int j = (int)(2); j <= (int)((M - 1) / i); j++) fl[i * j] = 1;
}
void add(int x, int y, int f) {
  e[++tot] = (edge){y, head[x], f};
  head[x] = tot;
  e[++tot] = (edge){x, head[y], 0};
  head[y] = tot;
}
bool bfs() {
  for (int i = (int)(1); i <= (int)(T); i++) dis[i] = -1;
  int h = 0, t = 1;
  q[1] = S;
  dis[S] = 0;
  while (h != t) {
    int x = q[++h];
    for (int i = head[x]; i; i = e[i].next)
      if (dis[e[i].to] == -1 && e[i].f) {
        dis[e[i].to] = dis[x] + 1;
        q[++t] = e[i].to;
      }
  }
  return dis[T] != -1;
}
int dfs(int x, int flow) {
  if (x == T) return flow;
  int k, rest = flow;
  for (int i = head[x]; i && rest; i = e[i].next)
    if (dis[e[i].to] == dis[x] + 1 && e[i].f) {
      k = dfs(e[i].to, min(rest, e[i].f));
      e[i].f -= k;
      e[i ^ 1].f += k;
      rest -= k;
    }
  if (rest) dis[x] = -1;
  return flow - rest;
}
void getans(int x, int be) {
  ans[be].push_back(x);
  vis[x] = 1;
  for (auto i : vec[x])
    if (!vis[i]) getans(i, be);
}
int main() {
  init();
  scanf("%d", &n);
  for (int i = (int)(1); i <= (int)(n); i++) {
    scanf("%d", &a[i]);
    ++SS[a[i] & 1];
  }
  if (SS[0] != SS[1]) return puts("Impossible"), 0;
  S = n + 1;
  T = S + 1;
  for (int i = (int)(1); i <= (int)(n); i++)
    if (a[i] & 1)
      add(i, T, 2);
    else
      add(S, i, 2);
  for (int i = (int)(1); i <= (int)(n); i++)
    for (int j = (int)(1); j <= (int)(n); j++)
      if (a[i] % 2 == 0 && !fl[a[i] + a[j]]) add(i, j, 1), id[i][j] = tot;
  for (; bfs(); sum += dfs(S, 1 << 30))
    ;
  if (sum != n) return puts("Impossible"), 0;
  for (int i = (int)(1); i <= (int)(n); i++)
    for (int j = (int)(1); j <= (int)(n); j++)
      if (id[i][j] && e[id[i][j]].f) vec[i].push_back(j), vec[j].push_back(i);
  for (int i = (int)(1); i <= (int)(n); i++)
    if (!vis[i]) getans(i, ++top);
  printf("%d\n", top);
  for (int i = (int)(1); i <= (int)(top); i++) {
    printf("%d", ans[i].size());
    for (auto j : ans[i]) printf(" %d", j);
    puts("");
  }
}