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;
template <typename T>
void read(T &x) {
  x = 0;
  int f(1);
  char c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') f = -1;
  for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
  x *= f;
}
const int maxn = 204;
const int inf = 0x3f3f3f3f;
int n, a[maxn], hd[maxn], tot;
int S, T, cnt, dis[maxn], pri[20005];
vector<int> ner[maxn], bel[maxn];
struct edge {
  int ed, nxt, f;
} e[2 * maxn * maxn];
void star(int u, int v, int F) {
  e[++cnt].ed = v;
  e[cnt].f = F;
  e[cnt].nxt = hd[u];
  hd[u] = cnt;
}
void g_prime();
bool bfs(int);
int dfs(int, int);
bool judge();
void g_cir(int);
int main() {
  read(n);
  cnt = 1;
  for (int i(1); i <= n; ++i) read(a[i]);
  S = n + 1;
  T = n + 2;
  g_prime();
  for (int i(1); i <= n; ++i) {
    if (a[i] & 1)
      star(S, i, 2), star(i, S, 0);
    else
      star(i, T, 2), star(T, i, 0);
  }
  for (int i(1); i <= n; ++i)
    if (a[i] & 1)
      for (int j(1); j <= n; ++j)
        if (a[j] % 2 == 0 && pri[a[i] + a[j]]) star(i, j, 1), star(j, i, 0);
  int ans = 0;
  while (bfs(S)) ans += dfs(S, inf);
  if (judge()) return puts("Impossible"), 0;
  for (int i = hd[S]; i; i = e[i].nxt) {
    int y = e[i].ed;
    for (int j = hd[y]; j; j = e[j].nxt) {
      int v = e[j].ed;
      if (v == S) continue;
      if (e[j].f == 0) ner[y].push_back(v), ner[v].push_back(y);
    }
  }
  memset(dis, 0, sizeof dis);
  for (int i(1); i <= n; ++i)
    if (!dis[i]) ++tot, g_cir(i);
  printf("%d\n", tot);
  for (int i(1); i <= tot; ++i) {
    printf("%d ", bel[i].size());
    for (int j(0); j < bel[i].size(); ++j) printf("%d ", bel[i][j]);
    printf("\n");
  }
  return 0;
}
void g_prime() {
  for (int i(3); i <= 20000; ++i) {
    if (i & 1) {
      pri[i] = 1;
      for (int j = 2; j <= floor(sqrt(i)); ++j)
        if (i % j == 0) {
          pri[i] = 0;
          break;
        }
    } else
      pri[i] = 0;
  }
}
bool bfs(int x) {
  memset(dis, 0, sizeof dis);
  dis[x] = 1;
  queue<int> q;
  q.push(x);
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int i = hd[u]; i; i = e[i].nxt) {
      int y = e[i].ed;
      if (e[i].f <= 0) continue;
      if (!dis[y] || dis[y] > dis[u] + 1) dis[y] = dis[u] + 1, q.push(y);
    }
  }
  return (dis[T] != 0);
}
int dfs(int x, int lowx) {
  if (x == T) return lowx;
  int ret = 0;
  for (int i = hd[x]; i; i = e[i].nxt) {
    int y = e[i].ed;
    if (dis[y] == dis[x] + 1 && e[i].f > 0) {
      int tmp = dfs(y, min(lowx, e[i].f));
      ret += tmp;
      lowx -= tmp;
      e[i].f -= tmp;
      e[i ^ 1].f += tmp;
      if (!lowx) break;
    }
  }
  return ret;
}
bool judge() {
  for (int i = hd[S]; i; i = e[i].nxt)
    if (e[i].f != 0) return 1;
  for (int i = hd[T]; i; i = e[i].nxt)
    if (e[i].f != 2) return 1;
  return 0;
}
void g_cir(int x) {
  dis[x] = 1;
  bel[tot].push_back(x);
  if (dis[ner[x][0]] && dis[ner[x][1]])
    return;
  else if (dis[ner[x][0]])
    g_cir(ner[x][1]);
  else
    g_cir(ner[x][0]);
}