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;
int n;
int nums[301];
vector<int> Graph[301];
int Flow[301][301];
int Cap[301][301];
int MaxFlow = 0;
int SOURCE, SINK;
vector<int> Tables[301];
int tL = 0;
void AddEdge(int a, int b) {
  Graph[a].push_back(b);
  Graph[b].push_back(a);
  Cap[a][b] = 1;
  Cap[b][a] = 0;
  Flow[a][b] = 0;
  Flow[b][a] = 0;
  return;
}
bool Prime(int a) {
  int i;
  for (i = 2; i * i <= a; i++) {
    if (a % i == 0) return false;
  }
  return true;
}
bool TFO[301];
vector<int> Path;
bool DFS(int ver) {
  if (TFO[ver]) return false;
  TFO[ver] = true;
  Path.push_back(ver);
  if (ver == SINK) return true;
  int i;
  for (i = 0; i < Graph[ver].size(); i++) {
    if (Flow[ver][Graph[ver][i]] < Cap[ver][Graph[ver][i]]) {
      if (DFS(Graph[ver][i])) return true;
    }
  }
  Path.pop_back();
  return false;
}
void SendFlow() {
  int i;
  for (i = 0; i < (int)Path.size() - 1; i++) {
    Flow[Path[i]][Path[i + 1]]++;
    Flow[Path[i + 1]][Path[i]]--;
  }
  MaxFlow++;
  return;
}
void Clear() {
  memset(TFO, false, sizeof(TFO));
  Path.clear();
  return;
}
void GetTable(int ver) {
  if (TFO[ver]) return;
  TFO[ver] = true;
  Tables[tL].push_back(ver);
  int i;
  for (i = 0; i < Graph[ver].size(); i++) {
    if (Flow[ver][Graph[ver][i]] != 0) {
      GetTable(Graph[ver][i]);
    }
  }
  return;
}
int main() {
  int i, j;
  int evens = 0, odds = 0;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &nums[i]);
    if (nums[i] % 2 == 0)
      evens++;
    else
      odds++;
  }
  if (evens != odds) {
    printf("Impossible\n");
    return 0;
  }
  for (i = 1; i <= n; i++) {
    for (j = i + 1; j <= n; j++) {
      if (Prime(nums[i] + nums[j])) {
        if (nums[i] % 2 == 0) {
          AddEdge(i, j);
        } else {
          AddEdge(j, i);
        }
      }
    }
  }
  SOURCE = n + 1;
  SINK = n + 2;
  for (i = 1; i <= n; i++) {
    if (nums[i] % 2 == 0) {
      Graph[SOURCE].push_back(i);
      Graph[i].push_back(SOURCE);
      Flow[SOURCE][i] = 0;
      Flow[i][SOURCE] = 0;
      Cap[SOURCE][i] = 2;
      Cap[i][SOURCE] = 0;
    } else {
      Graph[SINK].push_back(i);
      Graph[i].push_back(SINK);
      Flow[SINK][i] = 0;
      Flow[i][SINK] = 0;
      Cap[i][SINK] = 2;
      Cap[SINK][i] = 0;
    }
  }
  Clear();
  while (DFS(SOURCE)) {
    SendFlow();
    Clear();
  }
  if (MaxFlow != n) {
    printf("Impossible\n");
    return 0;
  }
  memset(TFO, false, sizeof(TFO));
  TFO[SINK] = true;
  TFO[SOURCE] = true;
  for (i = 1; i <= n; i++) {
    if (!TFO[i]) {
      tL++;
      GetTable(i);
    }
  }
  printf("%d\n", tL);
  for (i = 1; i <= tL; i++) {
    printf("%d", Tables[i].size());
    for (j = 0; j < Tables[i].size(); j++) {
      printf(" %d", Tables[i][j]);
    }
    printf("\n");
  }
  return 0;
}