You are given a multiset $S$ consisting of $n$ integers. You should perform the following three-step operation some number of times until a single integer remains in $S$.

1. Choose a multiset $T$ such that $T$ is a sub-multiset of $S$ and $|T| \ge 2$.
2. Erase the elements of $T$ from $S$.
3. Insert the value $\max(T) - \min(T)$ into $S$.

Find a sequence of operations that maximizes the integer left in $S$.

Input

The first line contains a single integer $n$ ($2 \le n \le 10^5$).

The second line contains $n$ integers $S_1, S_2, \ldots, S_n$ ($0 \le S_i \le 10^5$).

Output

On the first line, print a single integer $k$, the number of operations ($1 \le k \le n - 1$).

On each of the next $k$ lines, print an integer $m$, the size of the chosen multiset $T$, followed by $m$ integers $T_1, T_2, \ldots, T_m$, the multiset itself, in any order ($2 \le m \le n$).

Note that the operations are performed in the same order they are listed. So, for each operation, $T$ must be a sub-multiset of $S$ when all the preceding operations are performed.

Examples

Input 1

7
33 24 63 48 97 90 93

Output 1

4
3 33 93 90
2 63 60
2 48 24
3 97 24 3

Note

In the example, we can perform the following operations:

The underlined values in $S$ denote the inserted integers. After the fourth operation, $S$ is reduced to a single integer value of $94$. It can be shown that no other sequence of operations results in a larger value.