Codeforces 977D（思维）

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本文介绍了一个有趣的问题，即如何通过特定的数学操作（除以3或乘以2）重新排列一个整数序列，使其符合预定的规则。文章提供了一种有效的解决方案，利用排序算法根据数字中3的因子数量进行排序，并在相同3因子数量的情况下按数值大小排序。

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题面：

Polycarp likes to play with numbers. He takes some integer number $x$ , writes it down on the board, and then performs with it $n - 1$ operations of the two kinds:

divide the number $x$ by $3$ ( $x$ must be divisible by $3$ );
multiply the number $x$ by $2$ .

After each operation, Polycarp writes down the result on the board and replaces $x$ by the result. So there will be $n$ numbers on the board after all.

You are given a sequence of length $n$ — the numbers that Polycarp wrote down. This sequence is given in arbitrary order, i.e. the order of the sequence can mismatch the order of the numbers written on the board.

Your problem is to rearrange (reorder) elements of this sequence in such a way that it can match possible Polycarp's game in the order of the numbers written on the board. I.e. each next number will be exactly two times of the previous number or exactly one third of previous number.

It is guaranteed that the answer exists.

Input

The first line of the input contatins an integer number $n$ ( $2 \leq n \leq 100$ ) — the number of the elements in the sequence. The second line of the input contains $n$ integer numbers $a_{1}, a_{2}, \dots, a_{n}$ ( $1 \leq a_{i} \leq 3 \cdot 10^{18}$ ) — rearranged (reordered) sequence that Polycarp can wrote down on the board.

Output

Print $n$ integer numbers — rearranged (reordered) input sequence that can be the sequence that Polycarp could write down on the board.

It is guaranteed that the answer exists.

   Examples
  
     Input
     
      Copy
     
6
4 8 6 3 12 9

     Output
     
      Copy
     
9 3 6 12 4 8 

     Input
     
      Copy
     
4
42 28 84 126

     Output
     
      Copy
     
126 42 84 28 

     Input
     
      Copy
     
2
1000000000000000000 3000000000000000000

     Output
     
      Copy
     
3000000000000000000 1000000000000000000

Note

In the first example the given sequence can be rearranged in the following way: $[9, 3, 6, 12, 4, 8]$ . It can match possible Polycarp's game which started with $x = 9$ .

题目描述：给你一个被打乱的序列，每次操作，都要把这个数除以3或者乘2，使之变成下一个数，问你满足条件的原序列数。

题目分析：这道题有很多人直接用dfs搜索答案，事实上这题没有这么麻烦。

我们试分析，对于这个序列，因为3这个因数是要被除的，因此在整个序列中，3的个数必定是逐渐减少的。因此我们可以先统计所有数的3的个数，然后根据3的个数进行sort排序。而对于3的个数相同的时候，此时意味着不能进行除以3的操作，即只能进行*2的操作，因此，我们只需要将大的数排在后面即可。

#include <bits/stdc++.h>
#define maxn 105
using namespace std;
typedef long long ll;
int n;
ll a[maxn];
ll get_3(ll x){
    int cnt=0;
    while((x%3)==0) cnt++,x/=3;
    return cnt;
}
bool cmp(ll a,ll b){
    ll x=get_3(a),y=get_3(b);
    if(x==y) return a<b;
    return x>y;
}
int main()
{
    int n;
    cin>>n;
    for(int i=1;i<=n;i++) cin>>a[i];
    sort(a+1,a+1+n,cmp);
    for(int i=1;i<=n;i++){
        cout<<a[i]<<" ";
    }
    return 0;
}