import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }




void main() {
  try {
    for (; ; ) {
      const numCases = readInt();
      foreach (caseId; 0 .. numCases) {
        const N = readLong();
        const M = 2 * N - 1;
        
        long m = M;
        long phi = M;
        for (long p = 2; p^^2 <= m; ++p) {
          if (m % p == 0) {
            do {
              m /= p;
            } while (m % p == 0);
            phi = phi / p * (p - 1);
          }
        }
        if (m > 1) {
          phi = phi / m * (m - 1);
        }
        debug {
          writeln("phi = ", phi);
        }
        
        long[] divs;
        for (long d = 1; d^^2 <= phi; ++d) {
          if (phi % d == 0) {
            divs ~= d;
            if (d != phi / d) {
              divs ~= phi / d;
            }
          }
        }
        divs.sort;
        foreach (d; divs) {
          long x = 2, y = 1;
          for (long e = d; e; e >>= 1) {
            if (e & 1) (y *= x) %= M;
            (x *= x) %= M;
          }
          if (y == 1) {
            writeln(d);
            break;
          }
        }
      }
    }
  } catch (EOFException e) {
  }
}