Sasha grew up and went to first grade. To celebrate this event her mother bought her a multiplication table M with n rows and n columns such that M_{ij}=a_i ⋅ a_j where a_1, ..., a_n 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 a_1, ..., a_n. Help Sasha restore the array!

Input

The first line contains a single integer n (3 ⩽ n ⩽ 10^3), the size of the table. 

The next n lines contain n integers each. The j-th number of the i-th line contains the number M_{ij} (1 ≤ M_{ij} ≤ 10^9). The table has zeroes on the main diagonal, that is, M_{ii}=0.

Output

In a single line print n integers, the original array a_1, ..., a_n (1 ≤ a_i ≤ 10^9). It is guaranteed that an answer exists. If there are multiple answers, print any.

Examples

Input


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


2 2 3 1 2 

Input


3
0 99990000 99970002
99990000 0 99980000
99970002 99980000 0


Output


9999 10000 9998 
import java.util.*;
import java.io.*;

/*

 */

public class R586B
{

	public static void main(String[] args)
	{
//		int[] x = {270, 60, 100, 15, 238};
//		print(x);
		JS scan = new JS();
		int n = scan.nextInt();
		int[][] arr = new int[n][n];
		for(int i = 0; i < n; i++){
			for(int j = 0; j < n; j++){
				arr[i][j] = scan.nextInt();
			}
		}
		long g = arr[0][1];
		for(int i = 2; i < n; i++) g = gcd(g, arr[0][i]);
		long[] ans = new long[n];
		ans[0] = g;
		for(int i = 1; i < n; i++){
			ans[i] = arr[i][0]/g;
		}
//		System.out.println(Arrays.toString(ans));
		long[] mult = new long[n];
//		long[] div = new long[n];
//		long tot = 1;
		Arrays.fill(mult, 1);
//		Arrays.fill(div, 1);

		long sofar = 1;
		for(int i = 1; i < n-1; i++){
			long quot = arr[i][i+1]/ans[i]/ans[i+1]/sofar/sofar;
			long root = (long)(Math.sqrt(quot)+1e-9);
			ans[0] /= root;
//			System.out.println(root);
			mult[i] = root;
			sofar *= root;
		}
		long prefm = 1;
		for(int i = 0; i < n; i++){
			prefm *= mult[i];
			System.out.print(ans[i]*prefm+" ");
		}
	}
	
	static long gcd(long a, long b){
		if(b == 0) return a;
		return gcd(b, a%b);
	}
	
	static void print(int[] arr){
		for(int i = 0; i < arr.length; i++){
			for(int j = 0; j < arr.length; j++){
				if(i == j) System.out.print(0+" ");
				else System.out.print((arr[i]*arr[j])+" ");
			}
			System.out.println();
		}
	}
	
	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}

		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
}
