【CodeForces - 1034A】Enlarge GCD

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@题目描述 - English@

time limit per test: 1 second
memory limit per test: 256 megabytes

Mr. F has n positive integers, a1,a2,…,an.

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.

Input
The first line contains an integer n (2≤n≤3⋅10^5) — the number of integers Mr. F has.
The second line contains n integers, a1,a2,…,an (1≤ai≤1.5⋅10^7).

Output
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).

Examples

input
3
1 2 4
output
1

input
4
6 9 15 30
output
2

input
3
1 1 1
output
-1

Note
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.

@中文题意@

n个数，要你删掉最少的数，使得剩下的数的gcd大于所有n个数的gcd。
n<=3*10^5, 1<=ai<=1.5*10^7

@分析@

我们先用cnt[i]表示a里面有多少个数等于i。

把所有的数都除以它们的gcd，则问题变为：保留最多的数，使得它们的gcd不等于1。假设所有数都等于1，显然无解。假设某一数不等于1，则单独选择这一个数就是一个解， 所以一定有解。我们枚举保留下来的数的gcd为p，则可以保留下来的个数为$f(p)={\sum }_{p|x}^{x<=1.5\ast 10^7}$

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