# Problem G

Gear Wheels

Gear wheels can be connected to form chains, where the teeth of adjacent gears interlock. This helps to transmit rotary motion over a long distance.

Now, you have $N$ gear wheels arranged on a straight line, numbered from $1$ to $N$ from left to right. Gear wheel $i$ has $T_ i$ teeth.

If we connect gear wheel $i$ to gear wheel $j$, we can calculate the gear ratio as $T_ i / T_ j$ (or $T_ j / T_ i$). For the transmission to work perfectly, the gear ratio must be an integer.

You would like to form a longest chain of gear wheels such that the transmission between every pair of adjacent gear wheels works perfectly. Also, as moving the gears around is a lot of work, you are not allowed to reorder the gears on a chain. That is, if gear wheels $w_1, w_2, \ldots , w_ k$ are connected in this order from left to right, then $w_1 < w_2 < \ldots < w_ k$.

That is an easy task for you, so you would like to challenge
yourself further. On top of finding one longest chain of gear
wheels, you wish to find the *maximum
number* of longest chains of gear wheels that can be formed,
while each gear wheel can only be used in one chain.

## Input

The first line of input contains an integer $N$ $(1 \leq N \leq 1000)$, the number of gear wheels.

The next line contains $N$ integers $T_1, T_2, \ldots , T_ N$ $(1 \leq T_ i \leq 10^{18})$, the number of teeth on each gear wheel.

## Output

Output two integers $L$ and $C$ on the first line: the length of the longest chain of gear wheels that can be formed, and the maximum number of longest chains of gear wheels that can be formed.

Then, output $C$ lines, each containing $L$ integers. The $i$-th line should contain the indices of the gear wheels in the $i$-th longest chain of gear wheels, in increasing order.

If there are multiple valid answers, you may output any of them.

Sample Input 1 | Sample Output 1 |
---|---|

7 9 7 18 11 14 2 3 |
3 2 1 3 7 2 5 6 |

Sample Input 2 | Sample Output 2 |
---|---|

5 2 3 4 6 12 |
3 1 1 3 5 |