CF1034A.Enlarge GCD

Mr. F has $n$ positive integers, $a_1, a_2, \ldots, a_n$.

He thinks the greatest common divisor of these integers is too small. So he wants to enlarge it by removing some of the integers.

But this problem is too simple for him, so he does not want to do it by himself. If you help him, he will give you some scores in reward.

Your task is to calculate the minimum number of integers you need to remove so that the greatest common divisor of the remaining integers is bigger than that of all integers.

F 先生有 $n$ 个正整数：$a_1, a_2, \ldots, a_n$。

他认为这些整数的最大公约数（GCD）太小了，因此希望通过删除其中一部分整数来增大该最大公约数。

但这个问题对他而言过于简单，所以他不想自己动手解决。如果你帮助他解决，他将给予你一些分数作为奖励。

你的任务是：计算需要删除的最少整数个数，使得剩余整数的最大公约数严格大于原始所有 $n$ 个整数的最大公约数。

The first line contains an integer $n$ ($2 \leq n \leq 3 \cdot 10^5$) — the number of integers Mr. F has.

The second line contains $n$ integers, $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1.5 \cdot 10^7$).

第一行包含一个整数 $n$（$2 \leq n \leq 3 \cdot 10^5$）—— 表示 Mr. F 拥有的整数个数。

第二行包含 $n$ 个整数：$a_1, a_2, \ldots, a_n$（$1 \leq a_i \leq 1.5 \cdot 10^7$）。

Print an integer — the minimum number of integers you need to remove so that the greatest common divisor of the remaining integers is bigger than that of all integers.

You should not remove all of the integers.

If there is no solution, print «-1» (without quotes).

输出一个整数——为使剩余整数的最大公约数（GCD）大于所有整数的最大公约数，所需移除的最少整数个数。

你不应移除全部整数。

若无解，则输出 «-1»（不带引号）。

In the first example, the greatest common divisor is $1$ in the beginning. You can remove $1$ so that the greatest common divisor is enlarged to $2$. The answer is $1$.

In the second example, the greatest common divisor is $3$ in the beginning. You can remove $6$ and $9$ so that the greatest common divisor is enlarged to $15$. There is no solution which removes only one integer. So the answer is $2$.

In the third example, there is no solution to enlarge the greatest common divisor. So the answer is $-1$.

在第一个例子中，初始的最大公约数为 $1$。你可以移除 $1$，使得最大公约数扩大至 $2$。答案为 $1$。

在第二个例子中，初始的最大公约数为 $3$。你可以移除 $6$ 和 $9$，使得最大公约数扩大至 $15$。不存在仅移除一个整数的解。因此答案为 $2$。

在第三个例子中，不存在能使最大公约数扩大的解。因此答案为 $-1$。