import sys
input = lambda :sys.stdin.readline()[:-1]
ni = lambda :int(input())
na = lambda :list(map(int,input().split()))
sys.setrecursionlimit(10**7)
yes = lambda :print("yes");Yes = lambda :print("Yes")
no = lambda :print("no");No = lambda :print("No")
#######################################################################



pl = [2,3,5,7,11,13,17,19,23,29,31,37,41,43]
    


def f(x,y):
    r = 0
    while x>0:
        if x%y:
            break
        x//=y
        r+=1
    return r

def saiki(x, s, r):
    global S, ans
    #print(x,s,r)
    if s==S*2:
        #print(x,s,r)
        ans = min(ans, r)
    elif s>S*2:
        return 0
    t = 1
    if x>=len(z):
        return 0
    while s<=S*2 and r<=ans:
        saiki(x+1, s, r)
        s = s*(z[x][2]+t+1)//(z[x][2]+t)
        r *= z[x][1]
        t+=1
        
    

T = ni()
for i in range(T):
    x = ni()
    ans = 10**15
    z = []
    for t,j in enumerate(pl):
        ff = f(x,j)
        if ff>0:
            z.append((t, j, ff))
        if ff==0:
            mp = j
            mt = t
            ans = j
            break
    S = 1
    for i in z:
        S*=i[2]+1
    saiki(0, S, 1)
    print(x*ans)