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 PYTHON3):

Solution:
def main():
    sieve = [False, True] * 10001
    for i in range(3, 140, 2):
        if sieve[i]:
            j, k = i * 2, i * i
            le = (20001 - k) // j + 1
            sieve[k::j] = [False] * le

    n = int(input())
    aa = list(map(int, input().split()))
    pp = [-1] * n

    def dsu_get(v):
        if dsu[v] != v:
            dsu[v] = dsu_get(dsu[v])
        return dsu[v]

    def dfs(v):
        if free[v]:
            free[v], a, pv = False, aa[v], pp[v]
            for i, p in enumerate(pp):
                if sieve[a + aa[i]] and pv != i and (p == -1 or dfs(p)):
                    pp[i] = v
                    return True
        return False

    for i in range(n):
        free = [True] * n
        if not dfs(i):
            print('Impossible')
            return
    dsu = list(range(n))
    for i, p in enumerate(pp):
        i, p = dsu_get(i), dsu_get(p)
        dsu[p] = i

    print(sum(dsu_get(i) == i for i in range(n)))
    for i in range(n):
        if dsu_get(i) == i:
            row = [sum(dsu_get(j) == i for j in range(n)), i + 1]
            j = pp[i]
            while j != i:
                row.append(j + 1)
                j = pp[j]
            print(*row)


if __name__ == '__main__':
    main()



# Made By Mostafa_Khaled