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:
import math
def ip(x):
    for i in range(2,1 + int(math.sqrt(x))):
        if not x % i:
            return False
    return True

def add(x, y, z):
    cap[x][y] = z

def send(x, flow):
    if x == n + 1:
        return flow
    if vis[x]:
        return 0
    vis[x] = 1
    ret = 0
    for i in range(n + 2):
        if cap[x][i]:
            tmp = send(i, min(cap[x][i], flow))
            ret += tmp
            cap[x][i] -= tmp
            cap[i][x] += tmp
            flow -= tmp
            if not flow:
                return ret
    return ret

def flow():
    global vis
    ret = 0
    while(True):
        vis = [0 for i in range(n + 2)]
        tmp = send(n, n)
        ret += tmp
        if not tmp:
            break
    return ret

n = int(input())
a = [int(x) for x in input().split()]
odd = [1 if x % 2 else 0 for x in a]
even = [0 if x % 2 else 1 for x in a]
cap = [[0 for i in range(n+2)] for j in range(n+2)]
w = [[0 for i in range(n+2)] for j in range(n+2)]
if sum(odd) - sum(even):
    print("Impossible")
    exit()

for i in range(n):
    if odd[i]:
        add(n, i, 2)
        for j in range(n):
            if ip(a[i] + a[j]):
                add(i, j, 1)
    else:
        add(i, n + 1, 2)

if flow() == n:
    for i in range(n):
        for j in range(n):
            if odd[i] and cap[j][i]:
                w[i][j] = 1
                w[j][i] = 1
    ans = []
    vis = [0 for i in range(n)]
    for i in range(n):
        if not vis[i]:
            cur = i
            ans.append([])
            while not vis[cur]:
                ans[-1].append(cur + 1)
                vis[cur] = 1
                for j in range(n):
                    if w[cur][j] and not vis[j]:
                        cur = j
                        break
    print(len(ans))
    for x in ans:
        print("%d %s" % (len(x), " ".join([str(_) for _ in x])))
else:
    print("Impossible")