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>
inline t read(t &x) {
  char c = getchar();
  bool f = 0;
  x = 0;
  while (!isdigit(c)) f |= c == '-', c = getchar();
  while (isdigit(c)) x = (x << 1) + (x << 3) + (c ^ 48), c = getchar();
  if (f) x = -x;
  return x;
}
template <class t>
inline void write(t x) {
  if (x < 0)
    putchar('-'), write(-x);
  else {
    if (x > 9) write(x / 10);
    putchar('0' + x % 10);
  }
}
const int N = 205, M = 3e5 + 5;
int en = 1, h[N], cur[N], d[N], n, m, a[N];
vector<vector<int> > ans;
vector<int> vec, odd, even;
bool v[N];
struct edge {
  int n, v, w;
} e[M << 1];
void add(int x, int y, int z) {
  e[++en] = (edge){h[x], y, z};
  h[x] = en;
}
bool bfs(int s, int aim) {
  memset(d, 0, sizeof d);
  memcpy(cur, h, sizeof cur);
  queue<int> q;
  q.push(s);
  d[s] = 1;
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (int i = h[x]; i; i = e[i].n) {
      int y = e[i].v;
      if (!d[y] && e[i].w) {
        d[y] = d[x] + 1;
        if (y == aim) return 1;
        q.push(y);
      }
    }
  }
  return 0;
}
int dfs(int x, int flow, int aim) {
  if (x == aim) return flow;
  int rest = flow;
  for (int &i = cur[x]; i && rest; i = e[i].n) {
    int y = e[i].v;
    if (d[y] == d[x] + 1 && e[i].w) {
      int tp = dfs(y, min(rest, e[i].w), aim);
      rest -= tp;
      e[i].w -= tp;
      e[i ^ 1].w += tp;
    }
  }
  return flow - rest;
}
int dinic(int s, int t) {
  int res = 0;
  while (bfs(s, t)) res += dfs(s, INT_MAX, t);
  return res;
}
void exadd(int x, int y, int f) {
  add(x, y, f);
  add(y, x, 0);
}
bool isprime(int x) {
  for (int i = 2; i * i <= x; i++)
    if (x % i == 0) return 0;
  return 1;
}
void go(int x) {
  v[x] = 1;
  vec.push_back(x);
  for (int i = h[x]; i; i = e[i].n) {
    int y = e[i].v;
    if (v[y]) continue;
    if (!e[i ^ (a[x] & 1)].w) continue;
    go(y);
    break;
  }
}
signed main() {
  read(n);
  for (int i = 1; i <= n; i++) {
    read(a[i]);
    if (a[i] & 1)
      odd.push_back(i), exadd(0, i, 2);
    else
      even.push_back(i), exadd(i, n + 1, 2);
  }
  if (odd.size() != even.size()) {
    puts("Impossible");
    return 0;
  }
  for (int x : odd)
    for (int y : even)
      if (isprime(a[x] + a[y])) exadd(x, y, 1);
  if (dinic(0, n + 1) != n) {
    puts("Impossible");
    return 0;
  }
  v[0] = v[n + 1] = 1;
  for (int x : odd)
    if (!v[x]) {
      vec.clear();
      go(x);
      ans.push_back(vec);
    }
  write(ans.size());
  puts("");
  for (auto a : ans) {
    write(a.size());
    putchar(' ');
    for (int x : a) write(x), putchar(' ');
    puts("");
  }
}