Can you solve this keygen problem?

[dila]

bool check_key(uint64_t x) {
  uint64_t r = x;
  for (size_t i = 0; i < 64; ++i) {
    for (size_t j = 0; j < 6; ++j) {
      r ^= (((x >> (1 << j)) & (i >> j) & 1) << i);
    }
  }
  return (x && r == 0);
}

The objective is to find valid 64-bit input keys that make the function return 'true'.

1. How many valid input keys are there?
2. Can you make a generator to enumerate all valid keys?

Z3 (or other SMT/SAT) tools are not allowed as solutions!