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;
template <class T>
typename T::value_type arr_sum(const T& v, int n) {
  typename T::value_type sum = 0;
  for (int i = (0); i < (n); ++i) sum += v[i];
  return sum;
}
struct Sync_stdio {
  Sync_stdio() {
    cin.tie(NULL);
    ios_base::sync_with_stdio(false);
  }
} _sync_stdio;
const int INF = 2000000000;
struct edge {
  int a, b, cap, flow;
};
int n, s, t;
vector<int> d;
vector<int> ptr;
vector<int> q;
vector<edge> e;
vector<vector<int>> g;
vector<vector<int>> g2;
void add_edge(int a, int b, int cap) {
  edge e1 = {a, b, cap, 0};
  edge e2 = {b, a, 0, 0};
  g[a].push_back(e.size());
  e.push_back(e1);
  g[b].push_back(e.size());
  e.push_back(e2);
}
bool bfs() {
  int qh = 0, qt = 0;
  q[qt++] = s;
  d.assign(n + 2, -1);
  d[s] = 0;
  while (qh < qt && d[t] == -1) {
    int v = q[qh++];
    for (int i = 0; i < (int)g[v].size(); ++i) {
      int id = g[v][i];
      int to = e[id].b;
      if (d[to] == -1 && e[id].flow < e[id].cap) {
        q[qt++] = to;
        d[to] = d[v] + 1;
      }
    }
  }
  return d[t] != -1;
}
int dfs(int v, int flow) {
  if (!flow) {
    return 0;
  }
  if (v == t) {
    return flow;
  }
  for (; ptr[v] < (int)g[v].size(); ++ptr[v]) {
    int id = g[v][ptr[v]];
    int to = e[id].b;
    if (d[to] != d[v] + 1) {
      continue;
    }
    int pushed = dfs(to, min(flow, e[id].cap - e[id].flow));
    if (pushed) {
      e[id].flow += pushed;
      e[id ^ 1].flow -= pushed;
      return pushed;
    }
  }
  return 0;
}
int dinic() {
  int flow = 0;
  for (;;) {
    if (!bfs()) break;
    ptr.assign(n + 2, 0);
    while (int pushed = dfs(s, INF)) flow += pushed;
  }
  return flow;
}
vector<int> prime(100001, 1);
void get_primes(int n) {
  prime[0] = prime[1] = 0;
  int s = sqrt(n);
  for (int i = 2; i <= s; ++i) {
    if (prime[i]) {
      for (int j = i * i; j <= n; j += i) {
        prime[j] = 0;
      }
    }
  }
}
vector<vector<int>> comps;
vector<int> used;
void dfs2(int t) {
  comps[comps.size() - 1].push_back(t);
  used[t] = 1;
  for (auto i : g2[t]) {
    if (!used[i]) {
      dfs2(i);
    }
  }
}
void find_comps(vector<vector<int>>& g2) {
  for (int i = (0); i < (g2.size()); ++i) {
    if (used[i]) {
      continue;
    }
    comps.resize(comps.size() + 1);
    dfs2(i);
  }
}
int main() {
  cin >> n;
  g.resize(n + 2);
  used.resize(n);
  g2.resize(n);
  d.resize(n + 2);
  ptr.resize(n + 2);
  q.resize(n + 2);
  s = n;
  t = n + 1;
  get_primes(100000);
  vector<int> v(n);
  for (int i = 0; i < (n); ++i) cin >> v[i];
  ;
  int odd = 0;
  int even = 0;
  for (int i = (0); i < (n); ++i) {
    if (v[i] % 2) {
      ++odd;
    } else {
      ++even;
    }
  }
  if (odd != even) {
    cout << "Impossible"
         << "\n";
    return 0;
  }
  for (int i = (0); i < (n); ++i) {
    if (v[i] % 2) {
      add_edge(i, n + 1, 2);
    } else {
      add_edge(n, i, 2);
    }
    for (int j = (0); j < (n); ++j) {
      if (v[i] % 2) {
        continue;
      }
      if (prime[v[i] + v[j]]) {
        add_edge(i, j, 1);
      }
    }
  }
  if (dinic() != n) {
    cout << "Impossible"
         << "\n";
    return 0;
  }
  for (auto i : e) {
    if (i.flow == 1) {
      g2[i.a].push_back(i.b);
      g2[i.b].push_back(i.a);
    }
  }
  find_comps(g2);
  cout << comps.size() << "\n";
  for (auto i : comps) {
    cout << i.size() << " ";
    for (auto j : i) {
      cout << j + 1 << " ";
    }
    cout << "\n";
  }
}