# Python3 program to calculate # discrete logarithm import math; def discreteLogarithm(a, b, m): n = int(math.sqrt (m) + 1); # Calculate a ^ n an = 1; for i in range(n): an = (an * a) % m; value = [0] * m; # Store all values of a^(n*i) of LHS cur = an; for i in range(1, n + 1): if (value[ cur ] == 0): value[ cur ] = i; cur = (cur * an) % m; cur = b; for i in range(n + 1): # Calculate (a ^ j) * b and check # for collision if (value[cur] > 0): ans = value[cur] * n - i; if (ans < m): return ans; cur = (cur * a) % m; return -1; # A simple Python3 program # to calculate Euler's # Totient Function # Function to return # gcd of a and b def gcd(a, b): if (a == 0): return b return gcd(b % a, a) # Python3 program to calculate # Euler's Totient Function def phi(n): # Initialize result as n result = n; # Consider all prime factors # of n and subtract their # multiples from result p = 2; while(p * p <= n): # Check if p is a # prime factor. if (n % p == 0): # If yes, then # update n and result while (n % p == 0): n = int(n / p); result -= int(result / p); p += 1; # If n has a prime factor # greater than sqrt(n) # (There can be at-most # one such prime factor) if (n > 1): result -= int(result / n); return result; # This code is contributed # by mits t=int(input()) for _ in range(t): n=int(input()) if n==1: print(0) continue a=discreteLogarithm(2,1,2*n-1) totient=phi(2*n-1) while True: flag=0 count=2 while count*count<=totient: if totient%count==0 and pow(2,totient//count,2*n-1)==1: totient=totient//count break count+=1 if count*count>totient: flag=1 if flag==1: break print(totient)