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 MAXP = 100500;
bool is_prime[MAXP];
const int MAXN = 300;
int ans[MAXN];
int rev[MAXN];
int rev1[MAXN];
int sm[MAXN][MAXN];
int n, arr[MAXN];
bool used[MAXN];
void gen_primes() {
  for (int i = 0; i < MAXP; ++i) {
    is_prime[i] = true;
  }
  is_prime[0] = is_prime[1] = false;
  for (int i = 2; i * i < MAXP; ++i) {
    if (is_prime[i]) {
      for (int j = i * i; j < MAXP; j += i) {
        is_prime[j] = false;
      }
    }
  }
}
bool try_kuhn(int x) {
  if (used[x]) {
    return false;
  }
  used[x] = true;
  for (int j = 0; j < n; ++j) {
    if (sm[x][j]) {
      if (rev[j] == -1 || try_kuhn(rev[j])) {
        rev[j] = x;
        return true;
      }
    }
  }
  return false;
}
bool upd_kuhn(int x) {
  if (used[x]) {
    return false;
  }
  used[x] = true;
  for (int j = 0; j < n; ++j) {
    if (sm[x][j] && j != rev[x]) {
      if (rev[j] == -1 || upd_kuhn(rev[j])) {
        rev[j] = x;
        return true;
      }
    }
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  gen_primes();
  cin >> n;
  int odd = 0, even = 0;
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    if (arr[i] % 2 == 0) {
      odd++;
    } else {
      even++;
    }
  }
  for (int i = 0; i < n; ++i) {
    if (arr[i] % 2 == 1) {
      continue;
    }
    for (int j = 0; j < n; ++j) {
      if (is_prime[arr[i] + arr[j]]) {
        sm[i][j] = 1;
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    rev[i] = -1;
  }
  for (int i = 0; i < n; ++i) {
    if (arr[i] % 2 == 1) {
      continue;
    }
    memset(used, 0, sizeof(used[0]) * n);
    try_kuhn(i);
  }
  bool ok = true;
  for (int i = 0; i < n && ok; ++i) {
    if (arr[i] % 2 == 1 && rev[i] == -1) {
      ok = false;
    } else if (arr[i] % 2 == 1) {
      rev[rev[i]] = i;
    }
  }
  if (ok && odd == even) {
    for (int i = 0; i < n && ok; ++i) {
      if (arr[i] % 2 == 0) {
        continue;
      }
      int start = rev[i];
      if (rev[start] != i) {
        continue;
      }
      memset(used, 0, sizeof(used[0]) * n);
      rev[i] = -1;
      sm[start][i] = 0;
      if (!upd_kuhn(start)) {
        ok = false;
      }
      sm[start][i] = 1;
    }
    if (!ok) {
      cout << "Impossible\n";
    } else {
      vector<vector<int> > res;
      memset(used, 0, sizeof(used[0]) * n);
      for (int i = 0; i < n; ++i) {
        if (!used[i]) {
          vector<int> tmp;
          int cur = i;
          while (!used[cur]) {
            used[cur] = 1;
            tmp.push_back(cur);
            cur = rev[cur];
          }
          res.push_back(tmp);
        }
      }
      cout << res.size() << '\n';
      for (auto &tmp : res) {
        cout << tmp.size();
        for (auto x : tmp) {
          cout << " " << x + 1;
        }
        cout << '\n';
      }
    }
  } else {
    cout << "Impossible\n";
  }
  return 0;
}