Sieve

Giorgio is playing with the Sieve of Eratosthenes, one of the most ancient algorithms of all times. This algorithm starts with a row of all numbers from $2$ to $M$, then repeatedly selects the smallest non-selected number remaining in the row, erasing every multiple of it. At the end of the process, only prime numbers will have survived in the row!

Giorgio is trying to apply a similar idea, but with few differences. Firstly, some numbers are missing from the starting row, which contains only $N$ numbers overall (each of them between $2$ and $M$), in increasing order. Secondly, every time Giorgio selects a number, he erases not only the multiples of it but also its divisors. As in the original algorithm, Giorgio keeps selecting numbers from the row (end erasing accordingly), stopping when every remaining number has been already selected; but he doesn't have to select numbers in increasing order. How many numbers can remain at the end of the process, at minimum?

Input data

The first line of the input contains $N$ and $M$. The second line of the input contains the $N$ integers in increasing order.

Output data

The output file will contain a single line with an integer: the minimum amount of numbers that must remain at the end of the process.

Constraints and clarifications

• $1 \leq N \leq 250$
• $1 \leq M \leq 10^6$
• For tests worth $35$ points, $1 \leq N \leq 9$
• For tests worth $15$ more points, $1 \leq M \leq 20$
• For tests worth $20$ more points, $1 \leq N \leq 50$

Example 1

stdin

6 10
3 4 6 7 8 9

stdout

3

Explanation

In the first sample case, one of the best strategies is to choose numbers $7$, $3$ and $4$. Suboptimal solutions exist, such as choosing numbers $9$, $8$, $7$ and $6$.

Example 2

stdin

6 20
2 5 7 10 14 20

stdout

2

Explanation

In the second sample case, one of the best strategies is to choose numbers $20$ and $14$.