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 INF = 1000 * 1000 * 1000;
vector<vector<int>> potok(const vector<vector<int>>& c) {
  int n = c.size();
  int s = n - 2;
  int t = n - 1;
  vector<int> e(n);
  vector<int> h(n);
  h[s] = n - 1;
  vector<vector<int>> f(n, vector<int>(n));
  for (int i = 0; i < n; ++i) {
    f[s][i] = c[s][i];
    f[i][s] = -f[s][i];
    e[i] = c[s][i];
  }
  vector<int> maxh(n);
  int sz = 0;
  for (;;) {
    if (!sz)
      for (int i = 0; i < n; ++i)
        if (i != s && i != t && e[i] > 0) {
          if (sz && h[i] > h[maxh[0]]) sz = 0;
          if (!sz || h[i] == h[maxh[0]]) maxh[sz++] = i;
        }
    if (!sz) break;
    while (sz) {
      int i = maxh[sz - 1];
      bool pushed = false;
      for (int j = 0; j < n && e[i]; ++j)
        if (c[i][j] - f[i][j] > 0 && h[i] == h[j] + 1) {
          pushed = true;
          int addf = min(c[i][j] - f[i][j], e[i]);
          f[i][j] += addf, f[j][i] -= addf;
          e[i] -= addf, e[j] += addf;
          if (e[i] == 0) --sz;
        }
      if (!pushed) {
        h[i] = INF;
        for (int j = 0; j < n; ++j)
          if (c[i][j] - f[i][j] > 0 && h[j] + 1 < h[i]) h[i] = h[j] + 1;
        if (h[i] > h[maxh[0]]) {
          sz = 0;
          break;
        }
      }
    }
  }
  return f;
}
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  const int MAXA = 21000;
  vector<int> is_prime(MAXA, 1);
  is_prime[0] = 0;
  is_prime[1] = 0;
  for (int i = 2; i < MAXA; ++i) {
    if (!is_prime[i]) {
      continue;
    }
    for (int j = i * min(i, MAXA / i); j < MAXA; j += i) {
      if (i == j) {
        continue;
      }
      is_prime[j] = 0;
    }
  }
  vector<vector<int>> c(n + 2, vector<int>(n + 2));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (a[i] % 2 == 1) {
        continue;
      }
      if (a[j] % 2 == 0) {
        continue;
      }
      if (is_prime[a[i] + a[j]]) {
        c[i][j] = 1;
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    if (a[i] % 2 == 0) {
      c[n][i] = 2;
    } else {
      c[i][n + 1] = 2;
    }
  }
  vector<vector<int>> f = potok(c);
  int sum = 0;
  for (int i = 0; i < n; ++i) {
    sum += f[n][i];
  }
  if (sum != n) {
    cout << "Impossible" << endl;
    return 0;
  }
  vector<int> was(n);
  vector<vector<int>> anss;
  for (int i = 0; i < n; ++i) {
    if (!was[i]) {
      vector<int> ans = {i + 1};
      was[i] = 1;
      int next = -1;
      for (int j = 0; j < n; ++j) {
        if (f[i][j] != 0) {
          next = j;
          break;
        }
      }
      while (was[next] == 0) {
        was[next] = 1;
        ans.push_back(next + 1);
        for (int j = 0; j < n; ++j) {
          if (f[next][j] != 0 && was[j] == 0) {
            next = j;
            break;
          }
        }
      }
      anss.push_back(ans);
    }
  }
  cout << anss.size() << endl;
  for (int i = 0; i < anss.size(); ++i) {
    vector<int> ans = anss[i];
    cout << ans.size();
    for (int j = 0; j < ans.size(); ++j) {
      cout << " " << ans[j];
    }
    cout << endl;
  }
  return 0;
}