psx 0.1.8

Library for developing homebrew for the Sony PlayStation 1
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//! Fixed-point and trigonometry functions.

use core::hint::unreachable_unchecked;
use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

// TODO: Replace the derived Debug impl with a custom human-readable one
/// A signed 16-bit fixed-point number with 7-bit integral and 8-bit fractional
/// parts.
#[allow(non_camel_case_types)]
#[derive(Debug, Default, Copy, Clone, PartialOrd, Ord, PartialEq, Eq)]
pub struct f16(pub i16);

impl From<i8> for f16 {
    fn from(x: i8) -> Self {
        Self::from_int(x)
    }
}

impl f16 {
    /// The value 0.0 as an `f16`.
    pub const ZERO: Self = f16(0);

    /// The value 1.0 as an `f16`.
    pub const ONE: Self = f16::from_int(1);

    /// The number of integral bits.
    pub const INT: usize = 7;

    /// The number of fractional bits.
    pub const FRAC: usize = 8;

    /// Returns the absolute value of a number.
    pub const fn abs(self) -> Self {
        if self.0 & (1 << 15) == 0 {
            self
        } else {
            Self(-self.0)
        }
    }

    /// Converts an `i16` to fixed-point.
    pub const fn from_int(x: i8) -> Self {
        Self((x as i16) << f16::FRAC)
    }

    /// Converts to an `i16` keeping only the integral part and sign.
    pub const fn to_int_lossy(self) -> i16 {
        self.0 >> f16::FRAC
    }

    /// Returns the integer part of a number.
    pub const fn trunc(self) -> Self {
        Self(self.0 & (0xFF_00u16 as i16))
    }

    /// Returns the fractional part of a number.
    pub const fn fract(self) -> Self {
        Self(self.0 & 0x00_FF)
    }

    /// Raw transmutation to a `u16`.
    pub const fn to_bits(self) -> u16 {
        self.0 as u16
    }

    /// Raw transmutation from a `u16`.
    pub const fn from_bits(x: u16) -> Self {
        Self(x as i16)
    }
}

// TODO: Replace the derived Debug impl with a custom human-readable one
/// Radians scaled by `Ï€/0x8000`
///
/// This is a newtype for radians represented by a `u16` with `0x8000u16`
/// equaling π.
#[derive(Debug, Default, Copy, Clone, PartialOrd, Ord, PartialEq, Eq)]
pub struct Rad(pub u16);

/// π
pub const PI: Rad = Rad(0x8000);
/// π/2
pub const FRAC_PI_2: Rad = Rad(0x4000);
/// π/3
pub const FRAC_PI_3: Rad = Rad(0x2aaa);
/// π/4
pub const FRAC_PI_4: Rad = Rad(0x2000);
/// π/6
pub const FRAC_PI_6: Rad = Rad(0x1555);
/// π/8
pub const FRAC_PI_8: Rad = Rad(0x1000);

impl Neg for Rad {
    type Output = Rad;
    fn neg(self) -> Rad {
        Rad(-(self.0 as i16) as u16)
    }
}

impl Add<Rad> for Rad {
    type Output = Rad;
    fn add(self, other: Rad) -> Rad {
        Rad(self.0 + other.0)
    }
}

impl Sub<Rad> for Rad {
    type Output = Rad;
    fn sub(self, other: Rad) -> Rad {
        Rad(self.0 - other.0)
    }
}

impl Mul<u8> for Rad {
    type Output = Rad;
    fn mul(self, other: u8) -> Rad {
        Rad(self.0 * other as u16)
    }
}

impl Div<u8> for Rad {
    type Output = Rad;
    fn div(self, other: u8) -> Rad {
        Rad(self.0 / other as u16)
    }
}

impl AddAssign<Rad> for Rad {
    fn add_assign(&mut self, other: Rad) {
        *self = *self + other;
    }
}

impl SubAssign<Rad> for Rad {
    fn sub_assign(&mut self, other: Rad) {
        *self = *self - other;
    }
}

impl MulAssign<u8> for Rad {
    fn mul_assign(&mut self, other: u8) {
        *self = *self * other;
    }
}

impl DivAssign<u8> for Rad {
    fn div_assign(&mut self, other: u8) {
        *self = *self / other
    }
}

/// Rotates a point by `theta` radians about the x axis.
pub fn rotate_x([x, y, z]: [f16; 3], theta: Rad) -> [f16; 3] {
    let yp = (cos(theta) * y) - (sin(theta) * z);
    let zp = (sin(theta) * y) + (cos(theta) * z);
    [x, yp, zp]
}

/// Rotates a point by `theta` radians about the y axis.
pub fn rotate_y([x, y, z]: [f16; 3], theta: Rad) -> [f16; 3] {
    let xp = (cos(theta) * x) + (sin(theta) * z);
    let zp = (-sin(theta) * x) + (cos(theta) * z);
    [xp, y, zp]
}

/// Rotates a point by `theta` radians about the z axis.
pub fn rotate_z([x, y, z]: [f16; 3], theta: Rad) -> [f16; 3] {
    let xp = (cos(theta) * x) - (sin(theta) * y);
    let yp = (sin(theta) * x) + (cos(theta) * y);
    [xp, yp, z]
}

/// Computes the dot product of `a` and `b`.
pub fn dot(a: [f16; 3], b: [f16; 3]) -> f16 {
    (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2])
}

/// Computes sine using a lookup table.
pub fn sin(x: Rad) -> f16 {
    cos(FRAC_PI_2 - x)
}

/// Computes cosine using a lookup table.
pub fn cos(x: Rad) -> f16 {
    let quarter_cycle = FRAC_PI_2.0 as u16;
    let cycle = x.0 / quarter_cycle;
    let offset = x.0 % quarter_cycle;
    let idx = COSINE_TABLE_SIZE * (offset as usize) / quarter_cycle as usize;
    let rev_idx = COSINE_TABLE_SIZE - idx - 1;
    fn cosine_table(idx: usize) -> f16 {
        if idx == 0 {
            f16::ONE
        } else {
            // SAFETY: `idx` and `rev_idx` are always in a valid range
            let table_value = unsafe { *COSINE_TABLE.get_unchecked(idx - 1) } as u16;
            f16(table_value as i16)
        }
    }

    match cycle {
        0 => cosine_table(idx),
        1 => -cosine_table(rev_idx),
        2 => -cosine_table(idx),
        3 => cosine_table(rev_idx),
        _ => unsafe { unreachable_unchecked() },
    }
}

impl Neg for f16 {
    type Output = f16;
    fn neg(self) -> f16 {
        f16(-self.0)
    }
}
impl Add<f16> for f16 {
    type Output = f16;
    fn add(self, other: f16) -> f16 {
        f16(self.0 + other.0)
    }
}
impl Add<i8> for f16 {
    type Output = f16;
    fn add(self, other: i8) -> f16 {
        self + f16::from_int(other)
    }
}
impl Sub<f16> for f16 {
    type Output = f16;
    fn sub(self, other: f16) -> f16 {
        f16(self.0 - other.0)
    }
}
impl Sub<i8> for f16 {
    type Output = f16;
    fn sub(self, other: i8) -> f16 {
        self - f16::from_int(other)
    }
}
impl Mul<f16> for f16 {
    type Output = f16;
    fn mul(self, other: f16) -> f16 {
        let a = self.0 as i32;
        let b = other.0 as i32;
        let c = a * b;
        f16((c >> 8) as i16)
    }
}
impl Mul<i8> for f16 {
    type Output = f16;
    fn mul(self, other: i8) -> f16 {
        self * f16::from_int(other)
    }
}
impl Div<f16> for f16 {
    type Output = f16;
    fn div(self, other: f16) -> f16 {
        let num = (self.0 as i32) << 8;
        let den = other.0 as i32;
        let res = num / den;
        f16(res as i16)
    }
}
impl Div<i8> for f16 {
    type Output = f16;
    fn div(self, other: i8) -> f16 {
        self / f16::from_int(other)
    }
}
impl AddAssign<f16> for f16 {
    fn add_assign(&mut self, other: f16) {
        *self = *self + other;
    }
}
impl AddAssign<i8> for f16 {
    fn add_assign(&mut self, other: i8) {
        *self = *self + other;
    }
}
impl SubAssign<f16> for f16 {
    fn sub_assign(&mut self, other: f16) {
        *self = *self - other;
    }
}
impl SubAssign<i8> for f16 {
    fn sub_assign(&mut self, other: i8) {
        *self = *self - other;
    }
}
impl MulAssign<f16> for f16 {
    fn mul_assign(&mut self, other: f16) {
        *self = *self * other;
    }
}
impl MulAssign<i8> for f16 {
    fn mul_assign(&mut self, other: i8) {
        *self = *self * other;
    }
}
impl DivAssign<f16> for f16 {
    fn div_assign(&mut self, other: f16) {
        *self = *self / other;
    }
}
impl DivAssign<i8> for f16 {
    fn div_assign(&mut self, other: i8) {
        *self = *self / other;
    }
}

const COSINE_TABLE_SIZE: usize = 4096;
const COSINE_TABLE: [u8; COSINE_TABLE_SIZE - 1] = [
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
    255, 255, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254,
    254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254,
    254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254,
    254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254,
    254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254,
    254, 254, 254, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253,
    253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253,
    253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253,
    253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253, 253,
    252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252,
    252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252,
    252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252, 252,
    252, 252, 252, 252, 252, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251,
    251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251,
    251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251, 251,
    251, 251, 251, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250,
    250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250,
    250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 249, 249, 249, 249, 249,
    249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249,
    249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249, 249,
    249, 249, 249, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248,
    248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248, 248,
    248, 248, 248, 248, 248, 248, 248, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247,
    247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247, 247,
    247, 247, 247, 247, 247, 247, 247, 247, 247, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246,
    246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246, 246,
    246, 246, 246, 246, 246, 246, 246, 246, 246, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245,
    245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245, 245,
    245, 245, 245, 245, 245, 245, 245, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244,
    244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244, 244,
    244, 244, 244, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243,
    243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 242, 242,
    242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242,
    242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 242, 241, 241, 241, 241, 241, 241, 241, 241,
    241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241, 241,
    241, 241, 241, 241, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240,
    240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 239, 239, 239, 239, 239,
    239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239,
    239, 239, 239, 239, 239, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238,
    238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 238, 237, 237, 237, 237, 237,
    237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237, 237,
    237, 237, 237, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236,
    236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 236, 235, 235, 235, 235, 235, 235, 235, 235,
    235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 235, 234,
    234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234, 234,
    234, 234, 234, 234, 234, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233,
    233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 232, 232, 232, 232, 232, 232, 232, 232,
    232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 231, 231,
    231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231,
    231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230,
    230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229,
    229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228,
    228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227,
    227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226,
    226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226,
    226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225,
    225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224,
    224, 224, 224, 224, 224, 224, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223,
    223, 223, 223, 223, 223, 223, 223, 223, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 222,
    222, 222, 222, 222, 222, 222, 222, 222, 222, 222, 221, 221, 221, 221, 221, 221, 221, 221, 221,
    221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 221, 220, 220, 220, 220, 220, 220, 220, 220,
    220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 219, 219, 219, 219, 219, 219, 219,
    219, 219, 219, 219, 219, 219, 219, 219, 219, 219, 219, 219, 219, 218, 218, 218, 218, 218, 218,
    218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 217, 217, 217, 217, 217, 217,
    217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 216, 216, 216, 216, 216,
    216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 215, 215, 215, 215, 215,
    215, 215, 215, 215, 215, 215, 215, 215, 215, 215, 215, 215, 215, 215, 214, 214, 214, 214, 214,
    214, 214, 214, 214, 214, 214, 214, 214, 214, 214, 214, 214, 214, 213, 213, 213, 213, 213, 213,
    213, 213, 213, 213, 213, 213, 213, 213, 213, 213, 213, 213, 213, 212, 212, 212, 212, 212, 212,
    212, 212, 212, 212, 212, 212, 212, 212, 212, 212, 212, 212, 211, 211, 211, 211, 211, 211, 211,
    211, 211, 211, 211, 211, 211, 211, 211, 211, 211, 211, 210, 210, 210, 210, 210, 210, 210, 210,
    210, 210, 210, 210, 210, 210, 210, 210, 210, 210, 209, 209, 209, 209, 209, 209, 209, 209, 209,
    209, 209, 209, 209, 209, 209, 209, 209, 209, 208, 208, 208, 208, 208, 208, 208, 208, 208, 208,
    208, 208, 208, 208, 208, 208, 208, 207, 207, 207, 207, 207, 207, 207, 207, 207, 207, 207, 207,
    207, 207, 207, 207, 207, 207, 206, 206, 206, 206, 206, 206, 206, 206, 206, 206, 206, 206, 206,
    206, 206, 206, 206, 205, 205, 205, 205, 205, 205, 205, 205, 205, 205, 205, 205, 205, 205, 205,
    205, 205, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204, 204,
    203, 203, 203, 203, 203, 203, 203, 203, 203, 203, 203, 203, 203, 203, 203, 203, 203, 202, 202,
    202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 201, 201, 201, 201, 201,
    201, 201, 201, 201, 201, 201, 201, 201, 201, 201, 201, 201, 200, 200, 200, 200, 200, 200, 200,
    200, 200, 200, 200, 200, 200, 200, 200, 200, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199,
    199, 199, 199, 199, 199, 199, 199, 198, 198, 198, 198, 198, 198, 198, 198, 198, 198, 198, 198,
    198, 198, 198, 198, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197,
    197, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 195, 195,
    195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 194, 194, 194, 194, 194, 194,
    194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 193, 193, 193, 193, 193, 193, 193, 193, 193,
    193, 193, 193, 193, 193, 193, 193, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192,
    192, 192, 192, 191, 191, 191, 191, 191, 191, 191, 191, 191, 191, 191, 191, 191, 191, 191, 190,
    190, 190, 190, 190, 190, 190, 190, 190, 190, 190, 190, 190, 190, 190, 190, 189, 189, 189, 189,
    189, 189, 189, 189, 189, 189, 189, 189, 189, 189, 189, 188, 188, 188, 188, 188, 188, 188, 188,
    188, 188, 188, 188, 188, 188, 188, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187,
    187, 187, 187, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 185,
    185, 185, 185, 185, 185, 185, 185, 185, 185, 185, 185, 185, 185, 185, 184, 184, 184, 184, 184,
    184, 184, 184, 184, 184, 184, 184, 184, 184, 183, 183, 183, 183, 183, 183, 183, 183, 183, 183,
    183, 183, 183, 183, 183, 182, 182, 182, 182, 182, 182, 182, 182, 182, 182, 182, 182, 182, 182,
    181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 180, 180, 180, 180,
    180, 180, 180, 180, 180, 180, 180, 180, 180, 180, 179, 179, 179, 179, 179, 179, 179, 179, 179,
    179, 179, 179, 179, 179, 178, 178, 178, 178, 178, 178, 178, 178, 178, 178, 178, 178, 178, 178,
    178, 177, 177, 177, 177, 177, 177, 177, 177, 177, 177, 177, 177, 177, 177, 176, 176, 176, 176,
    176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 175, 175, 175, 175, 175, 175, 175, 175, 175,
    175, 175, 175, 175, 175, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174, 174,
    173, 173, 173, 173, 173, 173, 173, 173, 173, 173, 173, 173, 173, 173, 172, 172, 172, 172, 172,
    172, 172, 172, 172, 172, 172, 172, 172, 171, 171, 171, 171, 171, 171, 171, 171, 171, 171, 171,
    171, 171, 171, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 169, 169,
    169, 169, 169, 169, 169, 169, 169, 169, 169, 169, 169, 168, 168, 168, 168, 168, 168, 168, 168,
    168, 168, 168, 168, 168, 168, 167, 167, 167, 167, 167, 167, 167, 167, 167, 167, 167, 167, 167,
    166, 166, 166, 166, 166, 166, 166, 166, 166, 166, 166, 166, 166, 166, 165, 165, 165, 165, 165,
    165, 165, 165, 165, 165, 165, 165, 165, 164, 164, 164, 164, 164, 164, 164, 164, 164, 164, 164,
    164, 164, 163, 163, 163, 163, 163, 163, 163, 163, 163, 163, 163, 163, 163, 163, 162, 162, 162,
    162, 162, 162, 162, 162, 162, 162, 162, 162, 162, 161, 161, 161, 161, 161, 161, 161, 161, 161,
    161, 161, 161, 161, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 159, 159,
    159, 159, 159, 159, 159, 159, 159, 159, 159, 159, 159, 158, 158, 158, 158, 158, 158, 158, 158,
    158, 158, 158, 158, 158, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 156,
    156, 156, 156, 156, 156, 156, 156, 156, 156, 156, 156, 156, 155, 155, 155, 155, 155, 155, 155,
    155, 155, 155, 155, 155, 155, 154, 154, 154, 154, 154, 154, 154, 154, 154, 154, 154, 154, 153,
    153, 153, 153, 153, 153, 153, 153, 153, 153, 153, 153, 153, 152, 152, 152, 152, 152, 152, 152,
    152, 152, 152, 152, 152, 152, 151, 151, 151, 151, 151, 151, 151, 151, 151, 151, 151, 151, 150,
    150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 149, 149, 149, 149, 149, 149, 149,
    149, 149, 149, 149, 149, 149, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 147,
    147, 147, 147, 147, 147, 147, 147, 147, 147, 147, 147, 147, 146, 146, 146, 146, 146, 146, 146,
    146, 146, 146, 146, 146, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 144, 144,
    144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 143, 143, 143, 143, 143, 143, 143, 143,
    143, 143, 143, 143, 142, 142, 142, 142, 142, 142, 142, 142, 142, 142, 142, 142, 141, 141, 141,
    141, 141, 141, 141, 141, 141, 141, 141, 141, 140, 140, 140, 140, 140, 140, 140, 140, 140, 140,
    140, 140, 140, 139, 139, 139, 139, 139, 139, 139, 139, 139, 139, 139, 139, 138, 138, 138, 138,
    138, 138, 138, 138, 138, 138, 138, 138, 137, 137, 137, 137, 137, 137, 137, 137, 137, 137, 137,
    137, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 135, 135, 135, 135, 135, 135,
    135, 135, 135, 135, 135, 135, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 133,
    133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 132, 132, 132, 132, 132, 132, 132, 132,
    132, 132, 132, 132, 131, 131, 131, 131, 131, 131, 131, 131, 131, 131, 131, 131, 130, 130, 130,
    130, 130, 130, 130, 130, 130, 130, 130, 130, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129,
    129, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 127, 127, 127, 127, 127, 127,
    127, 127, 127, 127, 127, 127, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 125,
    125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 124, 124, 124, 124, 124, 124, 124, 124, 124,
    124, 124, 124, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 122, 122, 122, 122,
    122, 122, 122, 122, 122, 122, 122, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121,
    120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 119, 119, 119, 119, 119, 119, 119, 119,
    119, 119, 119, 119, 118, 118, 118, 118, 118, 118, 118, 118, 118, 118, 118, 117, 117, 117, 117,
    117, 117, 117, 117, 117, 117, 117, 117, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116,
    115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 114, 114, 114, 114, 114, 114, 114,
    114, 114, 114, 114, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 112, 112, 112, 112,
    112, 112, 112, 112, 112, 112, 112, 112, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111,
    110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 109, 109, 109, 109, 109, 109, 109, 109,
    109, 109, 109, 109, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 107, 107, 107, 107,
    107, 107, 107, 107, 107, 107, 107, 106, 106, 106, 106, 106, 106, 106, 106, 106, 106, 106, 105,
    105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 104, 104, 104, 104, 104, 104, 104, 104, 104,
    104, 104, 104, 103, 103, 103, 103, 103, 103, 103, 103, 103, 103, 103, 102, 102, 102, 102, 102,
    102, 102, 102, 102, 102, 102, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 100, 100,
    100, 100, 100, 100, 100, 100, 100, 100, 100, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 98,
    98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 96, 96, 96,
    96, 96, 96, 96, 96, 96, 96, 96, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 94, 94, 94, 94, 94,
    94, 94, 94, 94, 94, 94, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 92, 92, 92, 92, 92, 92, 92,
    92, 92, 92, 92, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 90, 90, 90, 90, 90, 90, 90, 90, 90,
    90, 90, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 87,
    87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 85, 85, 85,
    85, 85, 85, 85, 85, 85, 85, 85, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 83, 83, 83, 83, 83,
    83, 83, 83, 83, 83, 83, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 81, 81, 81, 81, 81, 81, 81, 81,
    81, 81, 81, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79,
    78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 76, 76,
    76, 76, 76, 76, 76, 76, 76, 76, 76, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 74, 74, 74, 74, 74,
    74, 74, 74, 74, 74, 74, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 72, 72, 72, 72, 72, 72, 72, 72,
    72, 72, 72, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70,
    69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 67, 67, 67,
    67, 67, 67, 67, 67, 67, 67, 67, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 65, 65, 65, 65, 65,
    65, 65, 65, 65, 65, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 63, 63, 63, 63, 63, 63, 63, 63,
    63, 63, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 60,
    60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 58, 58, 58, 58,
    58, 58, 58, 58, 58, 58, 58, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 56, 56, 56, 56, 56, 56, 56,
    56, 56, 56, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54,
    53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 51, 51, 51,
    51, 51, 51, 51, 51, 51, 51, 51, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 49, 49, 49, 49, 49, 49,
    49, 49, 49, 49, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 47, 47, 47, 47, 47, 47, 47, 47, 47,
    47, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 44, 44,
    44, 44, 44, 44, 44, 44, 44, 44, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 42, 42, 42, 42, 42, 42,
    42, 42, 42, 42, 42, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 40, 40, 40, 40, 40, 40, 40, 40, 40,
    40, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 37, 37,
    37, 37, 37, 37, 37, 37, 37, 37, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 35, 35, 35, 35, 35,
    35, 35, 35, 35, 35, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 33, 33, 33, 33, 33, 33, 33, 33, 33,
    33, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 30, 30,
    30, 30, 30, 30, 30, 30, 30, 30, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 28, 28, 28, 28, 28, 28,
    28, 28, 28, 28, 28, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 26, 26, 26, 26, 26, 26, 26, 26, 26,
    26, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 23,
    23, 23, 23, 23, 23, 23, 23, 23, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 21, 21, 21, 21, 21, 21,
    21, 21, 21, 21, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 19, 19, 19, 19, 19, 19, 19, 19, 19,
    19, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 16,
    16, 16, 16, 16, 16, 16, 16, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 14, 14, 14, 14, 14, 14,
    14, 14, 14, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
    11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9,
    9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6,
    6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3,
    3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0,
];