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;
namespace MF {
int n, m, s, t, to[(222 * 222)];
long long fl[(222 * 222)], cp[(222 * 222)];
int dst[222];
vector<int> al[222];
queue<int> q;
void init(int _n) {
  n = _n + 2;
  m = 0;
  s = _n;
  t = _n + 1;
  for (int i = (0); i < (n); i++) al[i].clear();
}
void add(int a, int b, long long c) {
  al[a].push_back(m);
  to[m] = b;
  fl[m] = 0;
  cp[m] = c;
  m++;
  al[b].push_back(m);
  to[m] = a;
  fl[m] = 0;
  cp[m] = 0;
  m++;
}
bool bfs() {
  for (int i = (0); i < (n); i++) dst[i] = i == s ? 0 : -1;
  q.push(s);
  while (!q.empty()) {
    int at = q.front();
    q.pop();
    for (int i = (0); i < (al[at].size()); i++) {
      int e = al[at][i];
      if (dst[to[e]] != -1 || fl[e] == cp[e]) continue;
      dst[to[e]] = dst[at] + 1;
      q.push(to[e]);
    }
  }
  return dst[t] != -1;
}
long long aug(int at, long long cf) {
  if (at == t) return cf;
  for (int i = (0); i < (al[at].size()); i++) {
    int e = al[at][i];
    if (dst[to[e]] != dst[at] + 1 || fl[e] == cp[e]) continue;
    long long tf = aug(to[e], min(cf, cp[e] - fl[e]));
    if (tf) {
      fl[e] += tf;
      fl[e ^ 1] -= tf;
      return tf;
    }
  }
  dst[at] = -1;
  return 0;
}
long long mf() {
  long long ans = 0;
  while (bfs())
    for (int add = aug(s, 1e18); add; add = aug(s, 1e18)) ans += add;
  return ans;
}
}  // namespace MF
int n, a[222], nt;
char notp[123456], s[222];
vector<int> tb[222];
void dfs(int at) {
  tb[nt].push_back(at);
  s[at] = 1;
  for (int i = (0); i < (MF::al[at].size()); i++) {
    int e = MF::al[at][i];
    if (!s[MF::to[e]] && MF::fl[e]) dfs(MF::to[e]);
  }
}
int main() {
  for (int i = 2; i * i < 123456; i++)
    if (!notp[i])
      for (int j = i * i; j < 123456; j += i) notp[j] = 1;
  scanf("%d", &n);
  for (int i = (0); i < (n); i++) scanf("%d", a + i);
  MF::init(n);
  for (int i = (0); i < (n); i++)
    (a[i] & 1) ? MF::add(MF::s, i, 2) : MF::add(i, MF::t, 2);
  for (int i = (0); i < (n); i++)
    if (a[i] & 1)
      for (int j = (0); j < (n); j++)
        if (!notp[a[i] + a[j]]) MF::add(i, j, 1);
  if (MF::mf() != n) {
    puts("Impossible");
    return 0;
  }
  s[n] = s[n + 1] = 1;
  for (int i = (0); i < (n); i++)
    if (!s[i]) {
      dfs(i);
      nt++;
    }
  printf("%d\n", nt);
  for (int i = (0); i < (nt); i++) {
    printf("%d ", tb[i].size());
    for (int j = (0); j < (tb[i].size()); j++) printf("%d ", tb[i][j] + 1);
    puts("");
  }
  return 0;
}