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 = 500500;
const int C = 3e4;
struct Edge {
  int from, to, cap, flow;
  Edge() {}
  Edge(int from, int to, int cap) : from(from), to(to), cap(cap), flow(0) {}
};
vector<int> h[N], e[N], v[2], w;
vector<Edge> g;
int n, m, ss, ff, isp[N], a[N], pr[N], used[N];
void add(int x, int y, int cap) {
  e[x].push_back(g.size());
  g.push_back(Edge(x, y, cap));
  e[y].push_back(g.size());
  g.push_back(Edge(y, x, 0));
}
bool way() {
  for (int i = 0; i <= ff; i++) pr[i] = -1;
  queue<int> q;
  q.push(ss);
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (int i = 0; i < e[x].size(); i++) {
      int id = e[x][i];
      int y = g[id].to;
      if ((g[id].flow < g[id].cap) && (pr[y] < 0)) {
        pr[y] = id;
        q.push(y);
      }
    }
  }
  if (pr[ff] == -1) return false;
  for (int i = ff; i != ss;) {
    int id = pr[i];
    g[id].flow++;
    g[id ^ 1].flow--;
    i = g[id].from;
  }
  return true;
}
void dfs(int x) {
  used[x] = true;
  w.push_back(x);
  for (int i = 0; i < h[x].size(); i++) {
    int y = h[x][i];
    if (!used[y]) dfs(y);
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    if (a[i] % 2 == 0) {
      v[0].push_back(i);
    } else {
      v[1].push_back(i);
    }
  }
  for (int i = 2; i < C; i++) isp[i] = true;
  for (int i = 2; i < C; i++) {
    if (isp[i]) {
      for (int j = i + i; j < C; j += i) isp[j] = false;
    }
  }
  if (v[0].size() != v[1].size()) {
    puts("Impossible");
    return 0;
  }
  for (int i = 0; i < v[0].size(); i++) {
    for (int j = 0; j < v[1].size(); j++) {
      if (isp[a[v[0][i]] + a[v[1][j]]]) {
        add(v[0][i], v[1][j], 1);
      }
    }
  }
  ss = n;
  ff = n + 1;
  for (int i = 0; i < v[0].size(); i++) add(ss, v[0][i], 2);
  for (int i = 0; i < v[1].size(); i++) add(v[1][i], ff, 2);
  while (way()) {
  }
  for (int i = 0; i < e[ss].size(); i++) {
    int id = e[ss][i];
    if (g[id].flow != g[id].cap) {
      puts("Impossible");
      return 0;
    }
  }
  for (int i = 0; i < v[0].size(); i++) {
    int x = v[0][i];
    for (int j = 0; j < e[x].size(); j++) {
      int id = e[x][j];
      if (g[id].flow > 0) {
        int y = g[id].to;
        if (y == ff) continue;
        h[x].push_back(y);
        h[y].push_back(x);
      }
    }
  }
  memset(used, 0, sizeof(used));
  vector<vector<int>> ans;
  for (int i = 0; i < n; i++) {
    if (!used[i]) {
      w.clear();
      dfs(i);
      ans.push_back(w);
    }
  }
  printf("%d\n", (int)ans.size());
  for (auto u : ans) {
    printf("%d ", (int)u.size());
    for (auto v : u) printf("%d ", 1 + v);
    puts("");
  }
}