B. Multiplication Table （ Codeforces Round #586 (Div. 1 + Div. 2) ）

Posted 2022-12-02 shallow-dream

Sasha grew up and went to first grade. To celebrate this event her mother bought her a multiplication table MM with nn rows and nn columns such that Mij=ai⋅ajMij=ai⋅aj where a1,…,ana1,…,an is some sequence of positive integers.

Of course, the girl decided to take it to school with her. But while she was having lunch, hooligan Grisha erased numbers on the main diagonal and threw away the array a1,…,ana1,…,an. Help Sasha restore the array!

Input

The first line contains a single integer nn (3?n?1033?n?103), the size of the table.

The next nn lines contain nn integers each. The jj-th number of the ii-th line contains the number MijMij (1≤Mij≤1091≤Mij≤109). The table has zeroes on the main diagonal, that is, Mii=0Mii=0.

Output

In a single line print nn integers, the original array a1,…,ana1,…,an (1≤ai≤1091≤ai≤109). It is guaranteed that an answer exists. If there are multiple answers, print any.

Examples

input

Copy

5
0 4 6 2 4
4 0 6 2 4
6 6 0 3 6
2 2 3 0 2
4 4 6 2 0

output

Copy

2 2 3 1 2 

input

Copy

3
0 99990000 99970002
99990000 0 99980000
99970002 99980000 0

output

Copy

9999 10000 9998 

 

 

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <string>
#include <cstring>
#include <cstdlib>
#include <map>
#include <vector>
#include <set>
#include <queue>
#include <stack>
#include <cmath>
using namespace std;
#define pq priority_queue<int>
#define pql priority_queue<ll>
#define pqn priority_queue<node>
#define v vector<int>
#define vl vector<ll>
#define lson rt<<1, l, m
#define rson rt<<1|1, m+1, r
#define read(x) scanf("%d",&x)
#define lread(x) scanf("%lld",&x);
#define pt(x) printf("%d\n",(x))
#define yes printf("YES\n");
#define no printf("NO\n");
#define gcd __gcd
#define out(x) cout<<x<<endl;
#define over cout<<endl;
#define rep(j,k) for (int i = (int)(j); i <= (int)(k); i++)
#define input(k) for (int i = 1; i <= (int)(k); i++)  cin>>a[i] ; 
#define mem(s,t) memset(s,t,sizeof(s))
#define re return ;
#define ok return 0;
#define TLE std::ios::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define mod(x) ((x)%9973)
#define test  cout<<"       ok             "<<endl;
#define ls now<<1
#define lli long long
const int mxn = 1e3+5;
lli a[mxn][mxn];
lli dp[mxn];
int gcd(int m, int n)

    while(m>0)
    
        int c = n % m;
        n = m;
        m = c;
    
    return n;

int main()

    TLE;
    int n,ans,cnt;
    string str;
    while(cin>>n)
    
        for(int i=1; i<=n; i++)
            for(int j=1; j<=n; j++)
            
                cin>>a[i][j];
            
        dp[1] = sqrt(a[1][2]*a[1][3]/a[2][3] );
        for(int i=2;i<=n;i++)
            dp[i] = a[1][i]/dp[1];
        cout<<dp[1];
        for(int i=2;i<=n;i++)
            cout<<" "<<dp[i];
        cout<<endl;
    
    ok;