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;
inline int read() {
  int x = 0, neg = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') neg = -1;
    c = getchar();
  }
  while (isdigit(c)) x = x * 10 + c - '0', c = getchar();
  return x * neg;
}
inline void print(int x) {
  if (x < 0) {
    putchar('-');
    print(abs(x));
    return;
  }
  if (x <= 9)
    putchar(x + '0');
  else {
    print(x / 10);
    putchar(x % 10 + '0');
  }
}
inline int qpow(int x, int e, int _MOD) {
  int ans = 1;
  while (e) {
    if (e & 1) ans = ans * x % _MOD;
    x = x * x % _MOD;
    e >>= 1;
  }
  return ans;
}
int head[100005];
struct edge {
  int to, nxt, cap;
} e[3000005];
int ecnt = 1;
inline void addedge(int u, int v, int f) {
  e[++ecnt].to = v;
  e[ecnt].cap = f;
  e[ecnt].nxt = head[u];
  head[u] = ecnt;
}
int dep[100005];
inline bool bfs(int s, int t) {
  queue<int> q;
  memset(dep, -1, sizeof(dep));
  q.push(s);
  dep[s] = 0;
  while (!q.empty()) {
    int cur = q.front();
    q.pop();
    for (int i = head[cur]; i; i = e[i].nxt) {
      int to = e[i].to;
      if (dep[to] == -1 && e[i].cap) {
        dep[to] = dep[cur] + 1;
        q.push(to);
      }
    }
  }
  if (dep[t] != -1) return 1;
  return 0;
}
inline int dfs(int x, int t, int f) {
  if (x == t) return f;
  int ret = 0;
  for (int i = head[x]; i; i = e[i].nxt) {
    int y = e[i].to;
    if (dep[y] == dep[x] + 1 && e[i].cap) {
      int w = dfs(y, t, min(f - ret, e[i].cap));
      e[i].cap -= w;
      e[i ^ 1].cap += w;
      ret += w;
      if (ret == f) return f;
    }
  }
  if (ret == 0) dep[x] = -1;
  return ret;
}
inline int Dinic(int s, int t) {
  int tot = 0;
  while (bfs(s, t)) tot += dfs(s, t, 0x3f3f3f3f);
  return tot;
}
int n = read(), a[205];
bool vis[20005];
inline void init() {
  for (int i = 2; i <= 20000; i++) {
    if (!vis[i]) {
      for (int j = i * 2; j <= 20000; j += i) {
        vis[j] = 1;
      }
    }
  }
}
vector<int> pth[205];
int ans = 0, used[205];
inline void dfss(int x) {
  pth[ans].push_back(x);
  used[x] = 1;
  for (int i = head[x]; i; i = e[i].nxt) {
    int y = e[i].to;
    if (y != 0 && y != (n + 1) && !used[y] && e[i | 1].cap == 1) {
      dfss(y);
    }
  }
}
signed main() {
  init();
  for (int i = 1; i <= n; i++) a[i] = read();
  for (int i = 1; i <= n; i++) {
    if (a[i] & 1) {
      addedge(0, i, 2);
      addedge(i, 0, 0);
    } else {
      addedge(i, n + 1, 2);
      addedge(n + 1, i, 0);
    }
  }
  for (int i = 1; i <= n; i++)
    if (a[i] & 1)
      for (int j = 1; j <= n; j++)
        if (a[i] ^ 1 & 1 && !vis[a[i] + a[j]]) {
          addedge(i, j, 1);
          addedge(j, i, 0);
        }
  if (Dinic(0, n + 1) != n) {
    puts("Impossible");
    return 0;
  }
  for (int i = 1; i <= n; i++)
    if (!used[i]) ans++, dfss(i);
  cout << ans << endl;
  for (int i = 1; i <= ans; i++) {
    cout << pth[i].size() << " ";
    for (__typeof(pth[i].begin()) it = pth[i].begin(); it != pth[i].end(); it++)
      cout << *it << " ";
    puts("");
  }
  return 0;
}