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 math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,copy,functools
# import time,random,resource

# sys.setrecursionlimit(10**6)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
mod2 = 998244353
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def pe(s): return print(str(s), file=sys.stderr)
def JA(a, sep): return sep.join(map(str, a))
def JAA(a, s, t): return s.join(t.join(map(str, b)) for b in a)
def IF(c, t, f): return t if c else f
def YES(c): return IF(c, "YES", "NO")
def Yes(c): return IF(c, "Yes", "No")


class Prime():
    def __init__(self, n):
        self.M = m = int(math.sqrt(n)) + 10
        self.A = a = [True] * m
        a[0] = a[1] = False
        self.T = t = [2]
        for j in range(4, m, 2):
            a[j] = False
        for i in range(3, m, 2):
            if not a[i]:
                continue
            t.append(i)
            for j in range(i*i,m,i):
                a[j] = False
        self.ds_memo = {}
        self.ds_memo[1] = set([1])

    def is_prime(self, n):
        return self.A[n]

    def division(self, n):
        d = collections.defaultdict(int)
        for c in self.T:
            while n % c == 0:
                d[c] += 1
                n //= c
            if n < 2:
                break
        if n > 1:
            d[n] += 1
        return d.items()

    # memo
    def divisions(self, n):
        if n in self.ds_memo:
            return self.ds_memo[n]

        for c in self.T:
            if n % c == 0:
                rs = set([c])
                for cc in self.divisions(n // c):
                    rs.add(cc)
                    rs.add(cc * c)
                self.ds_memo[n] = rs
                return rs

        rs = set([1, n])
        self.ds_memo[n] = rs
        return rs

def main():
    t = 1

    rr = []
    for _ in range(t):
        n = I()
        aa = [LI() for _ in range(n)]

        g = aa[0][1]
        for c in aa[0][2:]:
            g = math.gcd(g, c)

        r = []
        pr = Prime(g)
        for d in pr.divisions(g):
            t = [d]
            for c in aa[0][1:]:
                t.append(c//d)

            ok = 1
            for i in range(1,n):
                if not ok:
                    break
                for j in range(i+1,n):
                    if t[i] * t[j] != aa[i][j]:
                        ok = 0
                        break

            if ok:
                r = t
                break

        rr.append(JA(r, " "))

    return JA(rr, "\n")


print(main())


