Gym - 101911C Bacteria (规律题)

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Time limit2000 ms

Memory limit262144 kB

Recently Monocarp has created his own mini-laboratory!

The laboratory contains nn bacteria. Monocarp knows that he can merge any two bacteria having equal sizes, and the resulting bacterium will have the size equal to the sum of sizes of merged bacteria. For example, if two bacteria having sizes equal to 77 merge, one bacterium with size 1414 is the result.

It becomes hard to watch for many bacteria, so Monocarp wants to merge all of them into one bacterium. It may not be possible to do this with the bacteria Monocarp has, so he can buy any number of bacteria of any possible integer sizes in a special store.

You have to determine the minimum number of bacteria Monocarp has to buy to merge them with the nn bacteria his laboratory contains into exactly one bacterium.

Input

The first line contains one integer nn (1≤n≤2⋅105)(1≤n≤2⋅105) — the number of bacteria Monocarp's laboratory contains.

The second line contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤109)(1≤ai≤109), where aiai is the size of the ii-th bacterium in the laboratory.

Output

If it is impossible to merge the bacteria (possibly after buying some) into only one bacterium, print -1.

Otherwise print the minimum number of bacteria Monocarp has to buy to merge them with the nn bacteria his laboratory contains into exactly one bacterium.

Examples

Input

2
1 4

Output

2

Input

3
3 6 9

Output

-1

Input

7
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Output

1

Note

In the first example Monocarp should buy one bacterium having size 11 and one bacterium having size 22. Then Monocarp will have 44 bacteria having sizes [1,4,1,2][1,4,1,2]. Then two bacteria having sizes 11 can be merged into one having size 22. Then Monocarp will have 33 bacteria having sizes [2,4,2][2,4,2]. Then two bacteria having sizes 22 can be merged into one having size 44. Then Monocarp will have 22 bacteria having sizes [4,4][4,4], which can be merged into one having size 88.

In the second example no matter which bacteria Monocarp will buy, he cannot merge all his bacteria.

In the third example Monocarp needs to buy one bacterium having size 1000000000.

题意：给N个数，只有相同的两个数才能结合起来，加在一起。比如说2只有和2结合，成为4。

比如样例1的 1 4 ，我们需要加一个1，和原来的1结合，成为2，然后因为2没有可以组合的，所以再加一个2，组合成4，4和原来的4组合成为8。

询问的就是能不能通过添加一些数，最后能组合成1个数。如果不能输出-1，如果能输出还缺少的数的个数。

思路：

简单推理一下会发现，从小到大取，每2个数，后一个如果不是前一个的倍数，肯定不行。后一个除以前一个不是2次幂，也不行。

然后就是简单的推上去合并的问题了。这个过程用队列模拟一下。

代码：

#include<bits/stdc++.h>
using namespace std;
#define LL long long
using namespace std;
int main()
{
    priority_queue<LL,vector<LL>,greater<LL> >q;
    int n;
    scanf("%d",&n);
    for(int i = 0 ; i < n ; i++){
        LL x;
        scanf("%lld",&x);
        q.push(x);
    }
    LL ans = 0;
    while(q.size()>=2){
        LL f1 = q.top();q.pop();
        LL f2 = q.top();q.pop();
        if(f2%f1 != 0)return puts("-1"),0;
        LL d = f2/f1;
        if((d&(d-1))!=0) return puts("-1"),0;
        q.push(f2*2LL);
        ans += (LL)log2(f2*1.0/f1);
    }
    printf("%lld\n",ans);
}
/*
7
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

3
3 6 9

2
1 4
*/