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:
N = int(input())
L = list(map(int, input().split(' ')))

def isPrime(x) :
    for i in range(2, int(x**0.5)+2) :
        if x % i == 0 : return False
    return True

odd = []
even = []
for i in range(N) :
    if L[i]%2 == 0 :
        even.append(i)
    else :
        odd.append(i)

if len(odd) != len(even) :
    print("Impossible")
    exit()

cap = [[0]*(N+2) for i in range(N+2)]
for i in odd :
    cap[N][i] = 2
for i in even :
    cap[i][N+1] = 2
for i in odd :
    for j in even :
        if isPrime(L[i]+L[j]) :
            cap[i][j] = 1

def send(x, flow) :
    global visited, N
    if x == N+1 or flow == 0: return flow
    visited[x] = True
    ret = 0
    for nxt in range(N+2) :
        if visited[nxt] : continue
        if cap[x][nxt] == 0 : continue
        n_flow = min(cap[x][nxt], flow)
        n_flow = send(nxt, n_flow)
        flow -= n_flow
        ret += n_flow
        cap[x][nxt] -= n_flow
        cap[nxt][x] += n_flow
    return ret

flow = 0
while True :
    visited = [False]*(N+2)
    f = send(N, N)
    if f == 0 : break
    flow += f

if flow != N :
    print("Impossible")
    exit()

def dfs(x, path) :
    global visited, N, edge
    visited[x] = True
    ret = 1
    path.append(x)
    for nxt in edge[x] :
        if visited[nxt] : continue
        ret += dfs(nxt, path)
    return ret

visited = [False]*N
edge = [[] for i in range(N)]
for i in odd :
    for j in even :
        if cap[j][i] == 1 :
            edge[i].append(j)
            edge[j].append(i)
cnt = []
ans = []
for i in range(N) :
    if visited[i] == True : continue
    ans.append([])
    cnt.append(dfs(i, ans[-1]))

print(len(cnt))
for i in range(len(cnt)) :
    print(cnt[i], end = ' ')
    for j in ans[i] :
        print(j+1, end = ' ')
    print()