P=[2,3,5,7,11,13,17,19,23,29]

d=[[],[]]
for i in range(2,30):
  x=i
  c=[0]*len(P)
  for j in range(len(P)):
    p=P[j]
    while x%p==0:
      x//=p
      c[j]+=1
  d+=[[tuple([j,c[j]]) for j in range(len(P)) if c[j]>0]]

T=int(input())
for _ in range(T):
  X=int(input())
  x=X
  c=[0]*len(P)
  a=1
  for i in range(len(P)):
    p=P[i]
    while x%p==0:
      x//=p
      c[i]+=1
    a*=c[i]+1
  for i in range(2,30):
    b=a
    for j,e in d[i]:
      b//=c[j]+1
      b*=c[j]+e+1
    if a*2==b:
      print(X*i)
      break