GCD Table

GCD Table

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

The GCD table G of size n × n for an array of positive integers a of length n is defined by formula

Let us remind you that the greatest common divisor (GCD) of two positive integers x and y is the greatest integer that is divisor of both xand y, it is denoted as . For example, for array a = {4, 3, 6, 2} of length 4 the GCD table will look as follows:

Given all the numbers of the GCD table G, restore array a.

Input

The first line contains number n (1 ≤ n ≤ 500) — the length of array a. The second line contains n2 space-separated numbers — the elements of the GCD table of G for array a.

All the numbers in the table are positive integers, not exceeding 109. Note that the elements are given in an arbitrary order. It is guaranteed that the set of the input data corresponds to some array a.

Output

In the single line print n positive integers — the elements of array a. If there are multiple possible solutions, you are allowed to print any of them.

Sample test(s)

input

4
2 1 2 3 4 3 2 6 1 1 2 2 1 2 3 2

output

4 3 6 2

input

1
42

output

42 

input

2
1 1 1 1

output

1 1 

 模擬尋找過程，暴力就好：

　　　　　　首先num[]數組記錄各個值出現次數。

　　　　　　一定尋找最大值，num[]--,b[]數組記錄最大值，而後尋找次大值x，而且GCD求出y =  __gcd(b[],x),num[y] -= 2;

　　　　　　而後將其記錄在b[]數組中。

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
#include<map>
using namespace std;
int gcd(int x, int y){
    return y==0 ? x : gcd(y, x%y);
}
bool cmp(int x,int y){
    return x > y;
}
map<int, int>num;
int a[250005];
int b[505];
int main(){
    int n;
    scanf("%d",&n);
    for(int i = 0; i < n*n; i++){
        scanf("%d",&a[i]);
        num[a[i]]++;
    }
    int cnt = 0;
    sort(a,a+n*n,cmp);
    for(int i = 0; i < n*n; i++){
        if(!num[a[i]])continue;
        num[a[i]]--;
        for(int j = 0; j < cnt; j++){
            int x = gcd(a[i],b[j]);
            num[x] -= 2;
        }
        b[cnt++] = a[i];
    }
    for(int i = 0; i < n; i++){
        if(i)printf(" ");
        printf("%d",b[i]);
    }
    return 0;
}