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 = 209;
const int MAXNUM = 1e5 + 9;
const int INF = 1e9 + 33;
int numbers[MAXN];
vector<int> tab[MAXN];
bool prime[MAXNUM];
int przepustowosc[MAXN][MAXN];
vector<int> tab2[MAXN];
vector<int> spojne[MAXN];
int dp[MAXN];
bitset<MAXN> odw;
int dis[MAXN];
queue<int> Q;
int nr = 0;
void sito() {
  for (int i = 2; i < MAXNUM; i++) {
    prime[i] = true;
  }
  for (int i = 2; i < MAXNUM; i++) {
    if (!prime[i]) continue;
    for (int j = i + i; j < MAXNUM; j += i) prime[j] = false;
  }
}
void Add_Edge(int a, int b, int c) {
  przepustowosc[a][b] = c;
  tab[a].push_back(b);
  tab[b].push_back(a);
}
void dfs(int poz) {
  odw[poz] = 1;
  spojne[nr].push_back(poz);
  for (int i = 0; i < tab2[poz].size(); i++) {
    if (odw[tab2[poz][i]] == 0) dfs(tab2[poz][i]);
  }
}
bool bfs(int p, int k, int n) {
  int poz;
  fill(dis, dis + n, INF);
  dis[p] = 0;
  Q.push(p);
  while (!Q.empty()) {
    poz = Q.front();
    Q.pop();
    for (int i = 0; i < tab[poz].size(); i++) {
      if (przepustowosc[poz][tab[poz][i]] > 0) {
        if (dis[tab[poz][i]] > dis[poz] + 1) {
          dis[tab[poz][i]] = dis[poz] + 1;
          dp[tab[poz][i]] = poz;
          Q.push(tab[poz][i]);
        }
      }
    }
  }
  return dis[k] != INF;
}
int Edmonds_Karp(int s, int t, int n) {
  int mini, poz, wyn = 0;
  while (bfs(s, t, n)) {
    mini = INF;
    poz = t;
    while (poz != s) {
      mini = min(mini, przepustowosc[dp[poz]][poz]);
      poz = dp[poz];
    }
    poz = t;
    while (poz != s) {
      przepustowosc[dp[poz]][poz] -= mini;
      przepustowosc[poz][dp[poz]] += mini;
      poz = dp[poz];
    }
  }
  for (int i = 0; i < n - 1; i++) {
    wyn += przepustowosc[t][i];
  }
  return wyn;
}
int main() {
  int n;
  int even = 0;
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%d", &numbers[i]);
    if (numbers[i] % 2 == 0)
      even++;
    else
      even--;
    if (numbers[i] % 2 == 0)
      Add_Edge(0, i + 1, 2);
    else
      Add_Edge(i + 1, n + 1, 2);
  }
  if (even != 0) {
    puts("Impossible");
    return 0;
  }
  sito();
  for (int i = 0; i < n; i++) {
    if (numbers[i] % 2 == 1) continue;
    for (int j = 0; j < n; j++) {
      if (numbers[j] % 2 == 0) continue;
      if (prime[numbers[i] + numbers[j]]) {
        Add_Edge(i + 1, j + 1, 1);
      }
    }
  }
  int max_flow = Edmonds_Karp(0, n + 1, n + 2);
  if (max_flow != n) {
    puts("Impossible");
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (numbers[i] % 2 == 1) continue;
    for (int j = 0; j < n; j++) {
      if (numbers[j] % 2 == 0) continue;
      if (przepustowosc[j + 1][i + 1] == 1) {
        tab2[i + 1].push_back(j + 1);
        tab2[j + 1].push_back(i + 1);
      }
    }
  }
  odw.reset();
  for (int i = 1; i <= n; i++) {
    if (odw[i] == 0) {
      dfs(i);
      nr++;
    }
  }
  cout << nr << endl;
  for (int i = 0; i < nr; i++) {
    cout << spojne[i].size();
    for (int j = 0; j < spojne[i].size(); j++) {
      cout << " " << spojne[i][j];
    }
    cout << endl;
  }
  return 0;
}