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 N = 205;
const int s = 201, t = 202;
const int inf = 1000000000;
const int S = 20050;
struct Edge {
  int u, v, c;
  Edge() {}
  Edge(int a, int b, int d) {
    u = a;
    v = b;
    c = d;
  }
};
vector<Edge> edges;
vector<int> Network[N];
void AddEdge(int u, int v, int c) {
  Edge e;
  e = Edge(u, v, c);
  Network[u].push_back(edges.size());
  edges.push_back(e);
  e = Edge(v, u, 0);
  Network[v].push_back(edges.size());
  edges.push_back(e);
}
queue<int> q;
int par[N];
bool vis[N];
bool BFS() {
  int i;
  for (i = 0; i < N; i++) vis[i] = false;
  q.push(s);
  vis[s] = true;
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (i = 0; i < Network[x].size(); i++) {
      int e = Network[x][i];
      int v = edges[e].v;
      int c = edges[e].c;
      if (c && !vis[v]) {
        par[v] = e;
        vis[v] = true;
        q.push(v);
      }
    }
  }
  return vis[t];
}
int min(int a, int b) { return a > b ? b : a; }
int MaxFlow() {
  int Flow = 0, MinCut, i;
  while (BFS()) {
    MinCut = inf;
    for (i = t; i != s; i = edges[par[i]].u)
      MinCut = min(MinCut, edges[par[i]].c);
    Flow += MinCut;
    for (i = t; i != s; i = edges[par[i]].u) {
      edges[par[i]].c--;
      edges[par[i] ^ 1].c++;
    }
  }
  return Flow;
}
vector<int> Graph[N];
bool sieve[S];
void FindPrimes() {
  int i, j;
  for (i = 2; i < S; i++) {
    if (!sieve[i])
      for (j = i * 2; j < S; j += i) sieve[j] = true;
  }
}
int a[N];
int odd, even;
bool used[N];
vector<vector<int> > ans;
vector<int> tmp;
void DFS(int cur) {
  tmp.push_back(cur);
  used[cur] = true;
  int i;
  for (i = 0; i < Graph[cur].size(); i++) {
    int v = Graph[cur][i];
    if (!used[v]) DFS(v);
  }
}
int main() {
  int n, i, j;
  scanf("%i", &n);
  for (i = 1; i <= n; i++) {
    scanf("%i", &a[i]);
    if (a[i] & 1)
      odd++, AddEdge(i, t, 2);
    else
      even++, AddEdge(s, i, 2);
  }
  if (odd != even) return printf("Impossible\n"), 0;
  FindPrimes();
  for (i = 1; i <= n; i++) {
    if (a[i] % 2 == 0) {
      for (j = 1; j <= n; j++) {
        if (!sieve[a[i] + a[j]]) AddEdge(i, j, 1);
      }
    }
  }
  if (odd + even != MaxFlow()) return printf("Impossible\n"), 0;
  for (i = 1; i <= n; i++) {
    if (a[i] % 2 == 0) {
      for (j = 0; j < Network[i].size(); j++) {
        int e = Network[i][j];
        int v = edges[e].v;
        int c = edges[e].c;
        if (!c && v != s && v != t) {
          Graph[i].push_back(v);
          Graph[v].push_back(i);
        }
      }
    }
  }
  for (i = 1; i <= n; i++) {
    if (!used[i]) {
      tmp.clear();
      DFS(i);
      ans.push_back(tmp);
    }
  }
  printf("%i\n", ans.size());
  for (i = 0; i < ans.size(); i++) {
    printf("%i ", ans[i].size());
    for (j = 0; j < ans[i].size(); j++) printf("%i ", ans[i][j]);
    printf("\n");
  }
  return 0;
}