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 inf = 0x3fffffff;
const int maxn = 210;
const int maxm = 20500;
struct Node {
  int from, to, next;
  int cap;
} edge[maxm];
int tol;
int dep[maxn];
int head[maxn];
void init() {
  tol = 0;
  memset(head, -1, sizeof(head));
}
void addedge(int u, int v, int w) {
  edge[tol].from = u;
  edge[tol].to = v;
  edge[tol].cap = w;
  edge[tol].next = head[u];
  head[u] = tol++;
  edge[tol].from = v;
  edge[tol].to = u;
  edge[tol].cap = 0;
  edge[tol].next = head[v];
  head[v] = tol++;
}
int BFS(int start, int end) {
  int que[maxn];
  int front, rear;
  front = rear = 0;
  memset(dep, -1, sizeof(dep));
  que[rear++] = start;
  dep[start] = 0;
  while (front != rear) {
    int u = que[front++];
    if (front == maxn) front = 0;
    for (int i = head[u]; i != -1; i = edge[i].next) {
      int v = edge[i].to;
      if (edge[i].cap > 0 && dep[v] == -1) {
        dep[v] = dep[u] + 1;
        que[rear++] = v;
        if (rear >= maxn) rear = 0;
        if (v == end) return 1;
      }
    }
  }
  return 0;
}
int dinic(int start, int end) {
  int res = 0;
  int top;
  int stack[maxn];
  int cur[maxn];
  while (BFS(start, end)) {
    memcpy(cur, head, sizeof(head));
    int u = start;
    top = 0;
    while (1) {
      if (u == end) {
        int min = inf;
        int loc;
        for (int i = 0; i < top; i++)
          if (min > edge[stack[i]].cap) {
            min = edge[stack[i]].cap;
            loc = i;
          }
        for (int i = 0; i < top; i++) {
          edge[stack[i]].cap -= min;
          edge[stack[i] ^ 1].cap += min;
        }
        res += min;
        top = loc;
        u = edge[stack[top]].from;
      }
      for (int i = cur[u]; i != -1; cur[u] = i = edge[i].next)
        if (edge[i].cap != 0 && dep[u] + 1 == dep[edge[i].to]) break;
      if (cur[u] != -1) {
        stack[top++] = cur[u];
        u = edge[cur[u]].to;
      } else {
        if (top == 0) break;
        dep[u] = -1;
        u = edge[stack[--top]].from;
      }
    }
  }
  return res;
}
const int N = 2e4 + 100;
int prime[N];
bool is[N];
void getPrim() {
  for (int i = 2; i < N; i++) {
    if (!prime[i]) {
      prime[++prime[0]] = i;
    }
    for (int j = 1; (j <= prime[0]) && (i * prime[j] < N); j++) {
      prime[prime[j] * i] = 1;
      if (i % prime[j] == 0) break;
    }
  }
}
void get() {
  getPrim();
  memset(is, false, sizeof(is));
  for (int i = 1; i <= prime[0]; i++) is[prime[i]] = true;
}
int vis[maxn];
vector<int> V[maxn];
int a[maxn];
int ans;
int st, en;
int head1[maxn];
struct edge {
  int to, next;
} e[maxm];
int tol1 = 0;
void add(int u, int v) {
  e[++tol1].to = v, e[tol1].next = head1[u], head1[u] = tol1;
}
void dfs1(int u) {
  V[ans].push_back(u);
  vis[u] = 1;
  for (int i = head1[u]; i; i = e[i].next) {
    int v = e[i].to;
    if (vis[v]) continue;
    dfs1(v);
  }
}
int main() {
  init();
  get();
  int n;
  scanf("%d", &n);
  st = 0, en = n + 1;
  for (int i = 1; i < n + 1; i++) {
    scanf("%d", &a[i]);
    if (a[i] & 1)
      addedge(st, i, 2);
    else
      addedge(i, en, 2);
  }
  if (n & 1) {
    return 0 * puts("Impossible");
  }
  for (int i = 1; i < n + 1; i++) {
    for (int j = i + 1; j < n + 1; j++) {
      if ((a[i] & 1) && (a[j] % 2 == 0)) {
        if (is[a[i] + a[j]]) addedge(i, j, 1);
      }
      if ((a[i] % 2 == 0) && (a[j] & 1)) {
        if (is[a[i] + a[j]]) addedge(j, i, 1);
      }
    }
  }
  if (dinic(st, en) == n) {
    ans = 0;
    memset(vis, 0, sizeof(vis));
    for (int i = 1; i < tol; i += 2) {
      if (edge[i].cap == 1) {
        add(edge[i].to, edge[i].from), add(edge[i].from, edge[i].to);
      }
    }
    memset(vis, 0, sizeof(vis));
    for (int i = 1; i < n + 1; i++) {
      if (!vis[i]) ans++, dfs1(i);
    }
    printf("%d\n", ans);
    for (int i = 1; i < ans + 1; i++) {
      printf("%d", V[i].size());
      for (int j = 0; j < V[i].size(); j++) printf(" %d", V[i][j]);
      puts("");
    }
  } else
    puts("Impossible");
  return 0;
}