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>
#pragma comment(linker, "/STACK:128000000")
using namespace std;
void solve();
void precalc();
clock_t start;
bool doing = true;
int main() {
  int t = 1;
  cout.sync_with_stdio(0);
  cin.tie(0);
  precalc();
  cout.precision(10);
  cout << fixed;
  start = clock();
  int testNum = 1;
  while (t--) {
    solve();
  }
  return 0;
}
void precalc() {}
int binpow(int q, int w, int mod) {
  if (!w) return 1;
  if (w & 1) return q * binpow(q, w - 1, mod) % mod;
  return binpow(q * q % mod, w / 2, mod);
}
int gcd(int q, int w) {
  while (w) {
    q %= w;
    swap(q, w);
  }
  return q;
}
int n;
int a[210];
bool isPrime(int k) {
  for (int p = 2; p * p <= k; ++p) {
    if (k % p == 0) return false;
  }
  return true;
}
const int INF = 2e9;
struct edge {
  int from, to, cap, flow;
};
vector<edge> edges;
vector<int> g[300];
int q[300];
int d[300];
int ptr[300];
bool bfs(int s, int t) {
  memset(d, -1, sizeof d);
  int qh = 0, qt = 0;
  q[qt++] = s;
  d[s] = 0;
  while (qh != qt) {
    int cur = q[qh++];
    for (int i = 0; i < g[cur].size(); ++i) {
      edge& e = edges[g[cur][i]];
      if (e.flow != e.cap && d[e.to] == -1) {
        q[qt++] = e.to;
        d[e.to] = d[cur] + 1;
      }
    }
  }
  return d[t] != -1;
}
int dfs(int v, int t, int mx) {
  if (!mx) return mx;
  if (v == t) return mx;
  for (int& i = ptr[v]; i < g[v].size(); ++i) {
    int id = g[v][i];
    edge& e = edges[id];
    if (d[e.to] == d[v] + 1) {
      if (int pushed = dfs(e.to, t, min(mx, (e.cap - e.flow)))) {
        e.flow += pushed;
        edges[id ^ 1].flow -= pushed;
        return pushed;
      }
    }
  }
  return 0;
}
int dinic(int s, int t) {
  int res = 0;
  while (bfs(s, t)) {
    memset(ptr, 0, sizeof ptr);
    while (int pushed = dfs(s, t, INF)) {
      res += pushed;
    }
  }
  return res;
}
void add_edge(int from, int to, int cap) {
  edge e1 = {from, to, cap, 0};
  edge e2 = {to, from, 0, 0};
  g[from].push_back(edges.size());
  edges.push_back(e1);
  g[to].push_back(edges.size());
  edges.push_back(e2);
}
void solve() {
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  for (int i = 0; i < n; ++i) {
    for (int j = i + 1; j < n; ++j) {
      if (isPrime(a[i] + a[j])) {
        if (a[i] % 2 == 0) {
          add_edge(i, j, 1);
        } else {
          add_edge(j, i, 1);
        }
      }
    }
  }
  int s = n, t = n + 1;
  for (int i = 0; i < n; ++i) {
    if (a[i] % 2 == 0) {
      add_edge(s, i, 2);
    } else {
      add_edge(i, t, 2);
    }
  }
  int flow = dinic(s, t);
  if (flow != n) {
    cout << "Impossible\n";
    return;
  }
  vector<vector<int>> e(n);
  for (int i = 0; i < edges.size(); i += 2) {
    if (edges[i].flow == 1 && edges[i].cap == 1) {
      e[edges[i].from].push_back(edges[i].to);
      e[edges[i].to].push_back(edges[i].from);
    }
  }
  vector<vector<int>> ans;
  vector<int> have(n, false);
  for (int i = 0; i < n; ++i) {
    if (have[i]) continue;
    int cur = i;
    vector<int> curAns;
    while (!have[cur]) {
      have[cur] = true;
      curAns.push_back(cur);
      int nex = e[cur][0];
      if (have[nex]) {
        nex = e[cur][1];
      }
      cur = nex;
    }
    ans.push_back(curAns);
  }
  cout << ans.size() << "\n";
  for (int i = 0; i < ans.size(); ++i) {
    cout << ans[i].size() << ' ';
    for (int j = 0; j < ans[i].size(); ++j) {
      cout << ans[i][j] + 1 << ' ';
    }
    cout << "\n";
  }
}