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;
struct edge {
  int a, b, cap, flow;
};
int n, s, t, d[2601], ptr[2601], q[2601];
vector<edge> e;
vector<int> g[2601];
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((int)e.size());
  e.push_back(e1);
  g[b].push_back((int)e.size());
  e.push_back(e2);
}
bool bfs() {
  int qh = 0, qt = 0;
  q[qt++] = s;
  memset(d, -1, sizeof(d));
  d[s] = 0;
  while (qh < qt && d[t] == -1) {
    int v = q[qh++];
    for (unsigned int i = 0; i < g[v].size(); i++) {
      int id = g[v][i], to = e[id].b;
      if (d[v] != -1 && 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]], 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;
    }
    memset(ptr, 0, sizeof(ptr));
    while (int pushed = dfs(s, 1000000002)) {
      flow += pushed;
    }
  }
  return flow;
}
int m;
int a[501];
vector<pair<int, int> > even, odd;
bool prime(int a) {
  for (int i = 2; i <= (int)sqrt(a); i++) {
    if (a % i == 0) {
      return 0;
    }
  }
  return 1;
}
vector<int> c[1001];
vector<int> ans[1001];
bool used[1001];
int cnt = 0;
void dfs(int u) {
  used[u] = 1;
  if (u <= m) {
    ans[cnt].push_back(even[u - 1].second + 1);
  } else {
    ans[cnt].push_back(odd[u - m - 1].second + 1);
  }
  for (int i = 0; i < (int)c[u].size(); i++) {
    int h = c[u][i];
    if (!used[h]) {
      dfs(h);
    }
  }
}
int main() {
  cin >> m;
  for (int i = 0; i < m; i++) {
    cin >> a[i];
    if (a[i] % 2 == 0) {
      even.push_back(make_pair(a[i], i));
    } else {
      odd.push_back(make_pair(a[i], i));
    }
  }
  if ((int)even.size() != (int)odd.size()) {
    cout << "Impossible" << endl;
    return 0;
  }
  m /= 2;
  n = 2 * m + 2;
  s = 0;
  t = 2 * m + 1;
  for (int i = 1; i <= m; i++) {
    add_edge(s, i, 2);
  }
  for (int i = m + 1; i <= 2 * m; i++) {
    add_edge(i, t, 2);
  }
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < m; j++) {
      if (prime(even[i].first + odd[j].first)) {
        add_edge(i + 1, j + m + 1, 1);
      }
    }
  }
  dinic();
  int size = 0;
  for (int i = 0; i < (int)e.size(); i++) {
    if (e[i].a == s && e[i].b >= 1 && e[i].b <= m) {
      size += e[i].flow;
    }
  }
  if (size != 2 * m) {
    cout << "Impossible" << endl;
    return 0;
  }
  for (int i = 0; i < (int)e.size(); i++) {
    if (e[i].a >= 1 && e[i].a <= m && e[i].b >= m + 1 && e[i].b <= 2 * m) {
      if (e[i].flow == 1) {
        c[e[i].a].push_back(e[i].b);
        c[e[i].b].push_back(e[i].a);
      }
    }
  }
  for (int i = 1; i <= m; i++) {
    if (!used[i]) {
      dfs(i);
      cnt++;
    }
  }
  cout << cnt << endl;
  for (int i = 0; i < cnt; i++) {
    printf("%d", (int)ans[i].size());
    for (int j = 0; j < (int)ans[i].size(); j++) {
      printf(" %d", ans[i][j]);
    }
    printf("\n");
  }
  return 0;
}