import sys

# sys.setrecursionlimit(200005)
# sys.set_int_max_str_digits(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()

dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
inf = (1 << 63)-1
# md = 10**9+7
md = 998244353

def EulerPhi(n):
    res = n
    for i in range(2, n + 1):
        if i**2 > n: break
        if n % i == 0:
            res -= res // i
            while n % i == 0: n //= i
    if n > 1: res -= res // n
    return res

def factors(a):
    if a<=0:return [0]
    dd0,dd1=[],[]
    for d in range(1,round(a**0.5)+1):
        if a%d:continue
        dd0.append(d)
        dd1.append(a//d)
    if dd0[-1]==dd1[-1]:dd1.pop()
    return dd0+dd1[::-1]

def solve():
    n=II()
    if n==1:
        print(1)
        return 
    
    m=2*n-1
    for f in factors(EulerPhi(m)):
        if pow(2,f,m)==1:
            print(f)
            return
    print(-1)

for _ in range(II()):solve()