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;
const int MAXN = 205;
const int MAXM = 30005;
const int MAXV = 20005;
const int INF = 0x3f3f3f3f;
int prime[MAXV], pnum = 0;
bool isprime[MAXV];
void SievePrime() {
  isprime[0] = isprime[1] = false;
  for (int i = 2; i < MAXV; ++i) isprime[i] = true;
  for (int i = 2; i < MAXV; ++i) {
    if (isprime[i]) prime[pnum++] = i;
    for (int j = 0; j < pnum && i * prime[j] < MAXV; ++j) {
      isprime[i * prime[j]] = false;
      if (i % prime[j] == 0) break;
    }
  }
}
struct Edge {
  int to, next, cap, flow;
} edge[MAXM];
int tot, head[MAXN];
void init() {
  tot = 0;
  memset(head, 0xff, sizeof(head));
}
void addedge(int u, int v, int w, int rw = 0) {
  edge[tot].to = v;
  edge[tot].cap = w;
  edge[tot].flow = 0;
  edge[tot].next = head[u];
  head[u] = tot++;
  edge[tot].to = u;
  edge[tot].cap = rw;
  edge[tot].flow = 0;
  edge[tot].next = head[v];
  head[v] = tot++;
}
int gap[MAXN], dep[MAXN], pre[MAXN], cur[MAXN], src, sink, nodenum;
int sap() {
  memset(gap, 0, sizeof(gap));
  memset(dep, 0, sizeof(dep));
  memcpy(cur, head, sizeof(head));
  int u = src, ret = 0;
  pre[u] = -1;
  gap[0] = nodenum;
  while (dep[src] < nodenum) {
    if (u == sink) {
      int mindis = INF;
      for (int i = pre[u]; ~i; i = pre[edge[i ^ 1].to])
        mindis = min(mindis, edge[i].cap - edge[i].flow);
      for (int i = pre[u]; ~i; i = pre[edge[i ^ 1].to]) {
        edge[i].flow += mindis;
        edge[i ^ 1].flow -= mindis;
      }
      u = src;
      ret += mindis;
      continue;
    }
    bool flag = false;
    int v;
    for (int i = cur[u]; ~i; i = edge[i].next) {
      v = edge[i].to;
      if (edge[i].cap - edge[i].flow && dep[v] + 1 == dep[u]) {
        flag = true;
        cur[u] = pre[v] = i;
        break;
      }
    }
    if (flag) {
      u = v;
      continue;
    }
    int mindis = nodenum;
    for (int i = head[u]; ~i; i = edge[i].next) {
      v = edge[i].to;
      if (edge[i].cap - edge[i].flow && dep[v] < mindis) {
        mindis = dep[v];
        cur[u] = i;
      }
    }
    if (--gap[dep[u]] == 0) return ret;
    dep[u] = mindis + 1;
    ++gap[dep[u]];
    if (u != src) u = edge[pre[u] ^ 1].to;
  }
  return ret;
}
int a[MAXN];
bool vis[MAXN];
vector<int> g[MAXN];
vector<vector<int> > ans;
vector<int> tmp;
void dfs(int u) {
  vis[u] = true;
  tmp.push_back(u);
  for (int i = 0; i < g[u].size(); ++i)
    if (!vis[g[u][i]]) dfs(g[u][i]);
}
int main() {
  SievePrime();
  int n, cnt = 0;
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  init();
  src = 0;
  sink = n + 1;
  nodenum = n + 2;
  for (int i = 1; i <= n; ++i)
    if (a[i] & 1) {
      addedge(src, i, 2);
      for (int j = i + 1; j <= n; ++j)
        if (isprime[a[i] + a[j]]) addedge(i, j, 1);
    } else {
      addedge(i, sink, 2);
      for (int j = i + 1; j <= n; ++j)
        if (isprime[a[i] + a[j]]) addedge(j, i, 1);
      ++cnt;
    }
  if (sap() == cnt << 1) {
    for (int i = 1; i <= n; ++i)
      if (a[i] & 1)
        for (int j = head[i]; ~j; j = edge[j].next) {
          int v = edge[j].to;
          if (edge[j].flow && v >= 1 && v <= n) {
            g[i].push_back(v);
            g[v].push_back(i);
          }
        }
    memset(vis, false, sizeof(vis));
    for (int i = 1; i <= n; ++i)
      if (!vis[i]) {
        tmp.clear();
        dfs(i);
        ans.push_back(tmp);
      }
    printf("%d", ans.size());
    for (int i = 0; i < ans.size(); ++i) {
      printf("\n%d", ans[i].size());
      for (int j = 0; j < ans[i].size(); ++j) printf(" %d", ans[i][j]);
    }
  } else
    puts("Impossible");
}