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uint256 constant Q8 = 1 << 8;
uint256 constant Q16 = 1 << 16;
uint256 constant Q24 = 1 << 24;
uint256 constant Q32 = 1 << 32;
uint256 constant Q40 = 1 << 40;
uint256 constant Q48 = 1 << 48;
uint256 constant Q56 = 1 << 56;
uint256 constant Q64 = 1 << 64;
uint256 constant Q72 = 1 << 72;
uint256 constant Q80 = 1 << 80;
uint256 constant Q88 = 1 << 88;
uint256 constant Q96 = 1 << 96;
uint256 constant Q104 = 1 << 104;
uint256 constant Q112 = 1 << 112;
uint256 constant Q120 = 1 << 120;
uint256 constant Q128 = 1 << 128;