# 指定した整数以下の素数を列挙。エラトステネスの篩
def eratosthenes(n):
    l0=list(range(2,n+1))
    l1=[1]*(n+1)
    l1[0]=0
    l1[1]=0
    for li in l0:
        if li>int(n**0.5):
            break
        if l1[li]==1:
            k=2
        while k*li<=n:
            l1[k*li]=0
            k+=1
    ret=[i for i,li in enumerate(l1) if li==1]
    return ret

# 素因数分解
def factorization(n,prime):
    arr = []
    temp = n
    for p in prime:
        if temp%p==0:
            cnt=0
            while temp%p==0:
                cnt+=1
                temp //= p
            arr.append([p, cnt])
        if temp==1:break
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    ps={p:q for p,q in arr}
    return ps
prime=eratosthenes(31)
prime.sort()
df={i:factorization(i,prime) for i in range(2,32)}
t=int(input())
xx=[int(input()) for _ in range(t)]
inf=float('inf')

for x in xx:
    ps=factorization(x,prime)
    for i in range(2,32):
        if i not in ps:ps[i]=0
    nx=1
    ans=inf
    for v in ps.values():nx*=v+1
    for i in range(2,32):
        for k,v in df[i].items():ps[k]+=v
        ny=1
        for v in ps.values():ny*=v+1
        if 2*nx==ny:
            ans=x*i
            break
        for k,v in df[i].items():ps[k]-=v
    print(ans)