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 T {
  int a;
};
const int MAXN = 5000;
const int INF = 1000000000;
int nn;
vector<int> Ed[205];
struct dinic_maxflow {
  struct edge {
    int a, b, cap, flow;
    edge(int _a, int _b, int _cap, int _flow) {
      a = _a, b = _b, cap = _cap, flow = _flow;
    }
  };
  int n, s, t, d[MAXN], ptr[MAXN], q[MAXN];
  vector<edge> e;
  vector<int> g[MAXN];
  void add_edge(int a, int b, int cap) {
    edge e1 = edge(a, b, cap, 0);
    edge e2 = edge(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, n * sizeof d[0]);
    d[s] = 0;
    while (qh < qt && d[t] == -1) {
      int v = q[qh++];
      for (size_t i = 0; i < g[v].size(); ++i) {
        int id = g[v][i], 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]], 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, n * sizeof ptr[0]);
      while (int pushed = dfs(s, INF)) flow += pushed;
    }
    for (int i = 1; i <= nn; i++) {
      for (int j = 0; j < g[i].size(); j++) {
        if (e[g[i][j]].flow == 1 && e[g[i][j]].b > 0 && e[g[i][j]].b <= nn) {
          Ed[i].push_back(e[g[i][j]].b);
          Ed[e[g[i][j]].b].push_back(i);
        }
      }
    }
    return flow;
  }
  dinic_maxflow(int _n, int _s, int _t) {
    n = _n;
    s = _s;
    t = _t;
  }
};
int ar[205], vis[50000];
vector<int> aa[205];
int viss[205];
void dfs(int u, int t) {
  viss[u] = 1;
  aa[t].push_back(u);
  int i, j = Ed[u].size(), v;
  for (i = 0; i < j; i++) {
    v = Ed[u][i];
    if (viss[v] == 0) dfs(v, t);
  }
}
void prim() {
  int i = 0, j, n = sqrt(40000);
  memset(vis, 0, sizeof(vis));
  vis[1] = 1;
  for (i = 2; i <= n; i++) {
    if (vis[i] == 0) {
      for (j = i + i; j < 40000; j = j + i) {
        vis[j] = 1;
      }
    }
  }
}
int main() {
  int i, j, k, l, t, cs = 1, r = 1, s, m, n, a, b, c, d, e, f, g, h, u, v;
  prim();
  scanf("%d", &n);
  e = 0;
  for (i = 0; i < n; i++) {
    scanf("%d", &ar[i]);
    if (ar[i] % 2 == 0) e++;
  }
  dinic_maxflow dm = dinic_maxflow(300, 0, 250);
  for (i = 0; i < n; i++) {
    if (ar[i] % 2 == 1)
      dm.add_edge(0, i + 1, 2);
    else
      dm.add_edge(i + 1, 250, 2);
    for (j = 0; j < n; j++) {
      if (ar[i] % 2 == 1 && ar[j] % 2 == 0 && vis[ar[i] + ar[j]] == 0) {
        dm.add_edge(i + 1, j + 1, 1);
      }
    }
  }
  nn = n;
  h = dm.dinic();
  if (h == 2 * e && h == 2 * (n - e)) {
    memset(viss, 0, sizeof(viss));
    c = 0;
    for (i = 1; i <= n; i++) {
      if (viss[i] == 0) {
        dfs(i, c);
        c++;
      }
    }
    printf("%d\n", c);
    for (i = 0; i < c; i++) {
      printf("%d", aa[i].size());
      for (j = 0; j < aa[i].size(); j++) {
        printf(" %d", aa[i][j]);
      }
      printf("\n");
    }
  } else
    printf("Impossible\n");
  return 0;
}