== include(page="template/taskheader" task_id="tygyn") ==

Poveste şi cerinţă...

One of Marcel's ancestors, called Manchaary, son of Nyurgun and Sahayaana, was one of the servants of Tygyn Darkhan, at the beginning of the 17th century. Tygyn Darkhan, the great leader who unified the Yakutian tribes, seems to have been very passionate about Number Theory.

h2. Date de intrare

One day, he assigned some distinct integers from $2$ to $M$ to his $N$ cows. He decided to group the cows, based on their numbers, into as few herds as possible. However, he set the following conditions that should be met for all herds:

Fişierul de intrare $tygyn.in$ ...

* Let $x$ be the smallest number assigned to the cows in the herd. Each other number of a cow in the herd is of the form $x * k$, with $k$ integer.
* All divisors of $k$ (apart from $1$) are greater than or equal to any prime divisor of $x$, for all cows in the herd.

h2. Date de ieşire

However, Tygyn is a bit busy with keeping peace in his territory, so he asked Manchaary to take care of the cows. The task was rather difficult for Manchaary, but the reward was magnificent: he could then marry beautiful Sardaana!

În fişierul de ieşire $tygyn.out$ ...

We know the end of the story: Manchaary solved the task and Sardaana became an ancestor of Marcel. However, when Marcel learned about the story, he thought the task can go back  to the lands it originated. That is why the participants in Tuymaada 2019 have to solve it!

h2. Restricţii

h2. Input

* $... ≤ ... ≤ ...$

Input file $tygyn.in$ contains on the first line the integer numbers $N$ and $M$. The next line contains $N$ numbers with values between $2$ and $M$, representing the distinct numbers assigned to the $N$ cows of Tygyn Darkhan.

h2. Exemplu

h2. Output
 
Output file $tygyn.out$ contains the minimal number of herds Manchaary could group the cows into.
 
h2. Constraints
 
* $1 &le; N < M &le; 1.000.000$
* For $40$ points, $N &le; 1.000$
 
h2. Example

table(example). |_. tygyn.in |_. tygyn.out |

| This is some
  text written on
  multiple lines.
| This is another
  text written on
  multiple lines.

| 5 100
2 3 11 22 12
| 3

|

| 10 20
8 12 20 6 3 7 11 13 19 15
| 9
|

h3. Explicaţie

h3. Request

...

Contacteaza-l pe autor daca te oferi sa traduci enuntul in limba romana.

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