// Copyright (c) 2022 Marceline Cramer
// SPDX-License-Identifier: AGPL-3.0-or-later

// largely based on http://paulbourke.net/geometry/polygonise/
// TODO the Vec3 generic is pretty redundant, glam provides these types

use std::collections::HashMap;

#[derive(Copy, Clone, Debug, Eq, Hash, PartialEq)]
pub struct Vec3<T> {
    pub x: T,
    pub y: T,
    pub z: T,
}

impl<T: Copy> Vec3<T> {
    pub fn new(x: T, y: T, z: T) -> Self {
        Self { x, y, z }
    }

    pub fn to_array(&self) -> [T; 3] {
        [self.x, self.y, self.z]
    }
}

impl Vec3<f32> {
    pub fn to_glam(self) -> glam::Vec3A {
        glam::Vec3A::new(self.x, self.y, self.z)
    }
}

impl From<Vec3<i32>> for Vec3<f32> {
    fn from(other: Vec3<i32>) -> Self {
        Self {
            x: other.x as f32,
            y: other.y as f32,
            z: other.z as f32,
        }
    }
}

impl<T: Copy> From<Vec3<T>> for [T; 3] {
    fn from(other: Vec3<T>) -> Self {
        other.to_array()
    }
}

#[derive(Copy, Clone, Debug, Hash)]
pub struct MarchDomain {
    pub min: Vec3<i32>,
    pub max: Vec3<i32>,
}

#[derive(Copy, Clone, Debug)]
pub struct Vertex {
    pub position: Vec3<f32>,
    pub normal: Vec3<f32>,
}

// TODO support a set of march domains
// TODO use index buffer
// TODO cache shared vertices using HashMap<Edge, Vec3<f32>>
pub fn marching_cubes(
    scalar_field: impl Fn(i32, i32, i32) -> f32,
    domain: &MarchDomain,
) -> Vec<Vertex> {
    let samples = sample_corners(scalar_field, domain);

    let test = |corner| samples[&corner] > 0.0;

    // TODO this could be optimized using single-edge interpolation
    // TODO improve with glam vector math
    let interp = |cube: Vec3<i32>, edge_index| {
        let (c1, c2) = edge_coords(cube, edge_index);
        let v1 = samples[&c1];
        let v2 = samples[&c2];
        let p1: Vec3<f32> = c1.into();
        let p2: Vec3<f32> = c2.into();
        let mu = v1 / (v1 - v2);

        Vec3 {
            x: p1.x + mu * (p2.x - p1.x),
            y: p1.y + mu * (p2.y - p1.y),
            z: p1.z + mu * (p2.z - p1.z),
        }
    };

    let mut vertices = Vec::new();
    for x in domain.min.x..domain.max.x {
        for y in domain.min.y..domain.max.y {
            for z in domain.min.z..domain.max.z {
                let cube = Vec3::new(x, y, z);
                let index = configuration_index(cube, test);
                let edges = CUBE_CONFIGURATIONS[index];

                // TODO use Paul Bourke's edge table to share a cube's triangle vertices
                let mut ntriangle = 0;
                loop {
                    let e1 = edges[ntriangle];
                    if e1 < 0 {
                        break;
                    }

                    let p1 = interp(cube, e1);
                    let p2 = interp(cube, edges[ntriangle + 1]);
                    let p3 = interp(cube, edges[ntriangle + 2]);

                    let n = {
                        let p1 = p1.to_glam();
                        let p2 = p2.to_glam();
                        let p3 = p3.to_glam();

                        let n = (p2 - p1).cross(p3 - p1).normalize();

                        Vec3 {
                            x: n.x,
                            y: n.y,
                            z: n.z,
                        }
                    };

                    let n1 = n;
                    let n2 = n;
                    let n3 = n;

                    vertices.push(Vertex {
                        position: p1,
                        normal: n1,
                    });
                    vertices.push(Vertex {
                        position: p2,
                        normal: n2,
                    });
                    vertices.push(Vertex {
                        position: p3,
                        normal: n3,
                    });

                    ntriangle += 3;
                }
            }
        }
    }

    vertices
}

fn sample_corners(
    scalar_field: impl Fn(i32, i32, i32) -> f32,
    domain: &MarchDomain,
) -> HashMap<Vec3<i32>, f32> {
    let mut samples = HashMap::new();

    for x in domain.min.x..=domain.max.x {
        for y in domain.min.y..=domain.max.y {
            for z in domain.min.z..=domain.max.z {
                let s = scalar_field(x, y, z);
                let c = Vec3::new(x, y, z);
                samples.insert(c, s);
            }
        }
    }

    samples
}

#[rustfmt::skip]
fn corner_coords(cube: Vec3<i32>, corner_index: i8) -> Vec3<i32> {
    match corner_index {
        0 => cube,
        1 => Vec3 { y: cube.y + 1, ..cube },
        2 => Vec3 { x: cube.x + 1, y: cube.y + 1, ..cube },
        3 => Vec3 { x: cube.x + 1, ..cube },
        4 => Vec3 { z: cube.z + 1, ..cube },
        5 => Vec3 { y: cube.y + 1, z: cube.z + 1, ..cube },
        6 => Vec3 { x: cube.x + 1, y: cube.y + 1, z: cube.z + 1 },
        7 => Vec3 { x: cube.x + 1, z: cube.z + 1, ..cube },
        index => unreachable!("invalid corner index {}", index),
    }
}

fn edge_coords(cube: Vec3<i32>, edge_index: i8) -> (Vec3<i32>, Vec3<i32>) {
    let c = corner_coords;
    match edge_index {
        0 => (c(cube, 0), c(cube, 1)),
        1 => (c(cube, 1), c(cube, 2)),
        2 => (c(cube, 2), c(cube, 3)),
        3 => (c(cube, 3), c(cube, 0)),
        4 => (c(cube, 4), c(cube, 5)),
        5 => (c(cube, 5), c(cube, 6)),
        6 => (c(cube, 6), c(cube, 7)),
        7 => (c(cube, 7), c(cube, 4)),
        8 => (c(cube, 0), c(cube, 4)),
        9 => (c(cube, 1), c(cube, 5)),
        10 => (c(cube, 2), c(cube, 6)),
        11 => (c(cube, 3), c(cube, 7)),
        _ => unreachable!("invalid edge index"),
    }
}

fn configuration_index(cube: Vec3<i32>, test: impl Fn(Vec3<i32>) -> bool) -> usize {
    let s = |cube, corner| test(corner_coords(cube, corner)) as usize;
    s(cube, 0)
        | (s(cube, 1) << 1)
        | (s(cube, 2) << 2)
        | (s(cube, 3) << 3)
        | (s(cube, 4) << 4)
        | (s(cube, 5) << 5)
        | (s(cube, 6) << 6)
        | (s(cube, 7) << 7)
}

// source: http://paulbourke.net/geometry/polygonise/table2.txt
#[rustfmt::skip]
const CUBE_CONFIGURATIONS: [[i8; 13]; 256] = [
    [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 3, 0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 0, 1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 3, 1, 8, 1, 9,-1,-1,-1,-1,-1,-1,-1],
    [10, 1, 2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 3, 0, 1, 2,10,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 0, 2, 9, 2,10,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 2, 8, 2,10, 8, 8,10, 9,-1,-1,-1,-1],
    [11, 2, 3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [11, 2, 0,11, 0, 8,-1,-1,-1,-1,-1,-1,-1],
    [11, 2, 3, 0, 1, 9,-1,-1,-1,-1,-1,-1,-1],
    [ 2, 1,11, 1, 9,11,11, 9, 8,-1,-1,-1,-1],
    [10, 1, 3,10, 3,11,-1,-1,-1,-1,-1,-1,-1],
    [ 1, 0,10, 0, 8,10,10, 8,11,-1,-1,-1,-1],
    [ 0, 3, 9, 3,11, 9, 9,11,10,-1,-1,-1,-1],
    [ 8,10, 9, 8,11,10,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 4, 7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 0, 4, 3, 4, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 1, 9, 0, 8, 4, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 4, 1, 4, 7, 1, 1, 7, 3,-1,-1,-1,-1],
    [10, 1, 2, 8, 4, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 2,10, 1, 0, 4, 7, 0, 7, 3,-1,-1,-1,-1],
    [ 4, 7, 8, 0, 2,10, 0,10, 9,-1,-1,-1,-1],
    [ 2, 7, 3, 2, 9, 7, 7, 9, 4, 2,10, 9,-1],
    [ 2, 3,11, 7, 8, 4,-1,-1,-1,-1,-1,-1,-1],
    [ 7,11, 4,11, 2, 4, 4, 2, 0,-1,-1,-1,-1],
    [ 3,11, 2, 4, 7, 8, 9, 0, 1,-1,-1,-1,-1],
    [ 2, 7,11, 2, 1, 7, 1, 4, 7, 1, 9, 4,-1],
    [ 8, 4, 7,11,10, 1,11, 1, 3,-1,-1,-1,-1],
    [11, 4, 7, 1, 4,11, 1,11,10, 1, 0, 4,-1],
    [ 3, 8, 0, 7,11, 4,11, 9, 4,11,10, 9,-1],
    [ 7,11, 4, 4,11, 9,11,10, 9,-1,-1,-1,-1],
    [ 9, 5, 4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 0, 8, 4, 9, 5,-1,-1,-1,-1,-1,-1,-1],
    [ 5, 4, 0, 5, 0, 1,-1,-1,-1,-1,-1,-1,-1],
    [ 4, 8, 5, 8, 3, 5, 5, 3, 1,-1,-1,-1,-1],
    [ 2,10, 1, 9, 5, 4,-1,-1,-1,-1,-1,-1,-1],
    [ 0, 8, 3, 5, 4, 9,10, 1, 2,-1,-1,-1,-1],
    [10, 5, 2, 5, 4, 2, 2, 4, 0,-1,-1,-1,-1],
    [ 3, 4, 8, 3, 2, 4, 2, 5, 4, 2,10, 5,-1],
    [11, 2, 3, 9, 5, 4,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 5, 4, 8,11, 2, 8, 2, 0,-1,-1,-1,-1],
    [ 3,11, 2, 1, 5, 4, 1, 4, 0,-1,-1,-1,-1],
    [ 8, 5, 4, 2, 5, 8, 2, 8,11, 2, 1, 5,-1],
    [ 5, 4, 9, 1, 3,11, 1,11,10,-1,-1,-1,-1],
    [ 0, 9, 1, 4, 8, 5, 8,10, 5, 8,11,10,-1],
    [ 3, 4, 0, 3,10, 4, 4,10, 5, 3,11,10,-1],
    [ 4, 8, 5, 5, 8,10, 8,11,10,-1,-1,-1,-1],
    [ 9, 5, 7, 9, 7, 8,-1,-1,-1,-1,-1,-1,-1],
    [ 0, 9, 3, 9, 5, 3, 3, 5, 7,-1,-1,-1,-1],
    [ 8, 0, 7, 0, 1, 7, 7, 1, 5,-1,-1,-1,-1],
    [ 1, 7, 3, 1, 5, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 1, 2,10, 5, 7, 8, 5, 8, 9,-1,-1,-1,-1],
    [ 9, 1, 0,10, 5, 2, 5, 3, 2, 5, 7, 3,-1],
    [ 5, 2,10, 8, 2, 5, 8, 5, 7, 8, 0, 2,-1],
    [10, 5, 2, 2, 5, 3, 5, 7, 3,-1,-1,-1,-1],
    [11, 2, 3, 8, 9, 5, 8, 5, 7,-1,-1,-1,-1],
    [ 9, 2, 0, 9, 7, 2, 2, 7,11, 9, 5, 7,-1],
    [ 0, 3, 8, 2, 1,11, 1, 7,11, 1, 5, 7,-1],
    [ 2, 1,11,11, 1, 7, 1, 5, 7,-1,-1,-1,-1],
    [ 3, 9, 1, 3, 8, 9, 7,11,10, 7,10, 5,-1],
    [ 9, 1, 0,10, 7,11,10, 5, 7,-1,-1,-1,-1],
    [ 3, 8, 0, 7,10, 5, 7,11,10,-1,-1,-1,-1],
    [11, 5, 7,11,10, 5,-1,-1,-1,-1,-1,-1,-1],
    [10, 6, 5,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 3, 0,10, 6, 5,-1,-1,-1,-1,-1,-1,-1],
    [ 0, 1, 9, 5,10, 6,-1,-1,-1,-1,-1,-1,-1],
    [10, 6, 5, 9, 8, 3, 9, 3, 1,-1,-1,-1,-1],
    [ 1, 2, 6, 1, 6, 5,-1,-1,-1,-1,-1,-1,-1],
    [ 0, 8, 3, 2, 6, 5, 2, 5, 1,-1,-1,-1,-1],
    [ 5, 9, 6, 9, 0, 6, 6, 0, 2,-1,-1,-1,-1],
    [ 9, 6, 5, 3, 6, 9, 3, 9, 8, 3, 2, 6,-1],
    [ 3,11, 2,10, 6, 5,-1,-1,-1,-1,-1,-1,-1],
    [ 6, 5,10, 2, 0, 8, 2, 8,11,-1,-1,-1,-1],
    [ 1, 9, 0, 6, 5,10,11, 2, 3,-1,-1,-1,-1],
    [ 1,10, 2, 5, 9, 6, 9,11, 6, 9, 8,11,-1],
    [11, 6, 3, 6, 5, 3, 3, 5, 1,-1,-1,-1,-1],
    [ 0, 5, 1, 0,11, 5, 5,11, 6, 0, 8,11,-1],
    [ 0, 5, 9, 0, 3, 5, 3, 6, 5, 3,11, 6,-1],
    [ 5, 9, 6, 6, 9,11, 9, 8,11,-1,-1,-1,-1],
    [10, 6, 5, 4, 7, 8,-1,-1,-1,-1,-1,-1,-1],
    [ 5,10, 6, 7, 3, 0, 7, 0, 4,-1,-1,-1,-1],
    [ 5,10, 6, 0, 1, 9, 8, 4, 7,-1,-1,-1,-1],
    [ 4, 5, 9, 6, 7,10, 7, 1,10, 7, 3, 1,-1],
    [ 7, 8, 4, 5, 1, 2, 5, 2, 6,-1,-1,-1,-1],
    [ 4, 1, 0, 4, 5, 1, 6, 7, 3, 6, 3, 2,-1],
    [ 9, 4, 5, 8, 0, 7, 0, 6, 7, 0, 2, 6,-1],
    [ 4, 5, 9, 6, 3, 2, 6, 7, 3,-1,-1,-1,-1],
    [ 7, 8, 4, 2, 3,11,10, 6, 5,-1,-1,-1,-1],
    [11, 6, 7,10, 2, 5, 2, 4, 5, 2, 0, 4,-1],
    [11, 6, 7, 8, 0, 3, 1,10, 2, 9, 4, 5,-1],
    [ 6, 7,11, 1,10, 2, 9, 4, 5,-1,-1,-1,-1],
    [ 6, 7,11, 4, 5, 8, 5, 3, 8, 5, 1, 3,-1],
    [ 6, 7,11, 4, 1, 0, 4, 5, 1,-1,-1,-1,-1],
    [ 4, 5, 9, 3, 8, 0,11, 6, 7,-1,-1,-1,-1],
    [ 9, 4, 5, 7,11, 6,-1,-1,-1,-1,-1,-1,-1],
    [10, 6, 4,10, 4, 9,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 3, 0, 9,10, 6, 9, 6, 4,-1,-1,-1,-1],
    [ 1,10, 0,10, 6, 0, 0, 6, 4,-1,-1,-1,-1],
    [ 8, 6, 4, 8, 1, 6, 6, 1,10, 8, 3, 1,-1],
    [ 9, 1, 4, 1, 2, 4, 4, 2, 6,-1,-1,-1,-1],
    [ 1, 0, 9, 3, 2, 8, 2, 4, 8, 2, 6, 4,-1],
    [ 2, 4, 0, 2, 6, 4,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 2, 8, 8, 2, 4, 2, 6, 4,-1,-1,-1,-1],
    [ 2, 3,11, 6, 4, 9, 6, 9,10,-1,-1,-1,-1],
    [ 0,10, 2, 0, 9,10, 4, 8,11, 4,11, 6,-1],
    [10, 2, 1,11, 6, 3, 6, 0, 3, 6, 4, 0,-1],
    [10, 2, 1,11, 4, 8,11, 6, 4,-1,-1,-1,-1],
    [ 1, 4, 9,11, 4, 1,11, 1, 3,11, 6, 4,-1],
    [ 0, 9, 1, 4,11, 6, 4, 8,11,-1,-1,-1,-1],
    [11, 6, 3, 3, 6, 0, 6, 4, 0,-1,-1,-1,-1],
    [ 8, 6, 4, 8,11, 6,-1,-1,-1,-1,-1,-1,-1],
    [ 6, 7,10, 7, 8,10,10, 8, 9,-1,-1,-1,-1],
    [ 9, 3, 0, 6, 3, 9, 6, 9,10, 6, 7, 3,-1],
    [ 6, 1,10, 6, 7, 1, 7, 0, 1, 7, 8, 0,-1],
    [ 6, 7,10,10, 7, 1, 7, 3, 1,-1,-1,-1,-1],
    [ 7, 2, 6, 7, 9, 2, 2, 9, 1, 7, 8, 9,-1],
    [ 1, 0, 9, 3, 6, 7, 3, 2, 6,-1,-1,-1,-1],
    [ 8, 0, 7, 7, 0, 6, 0, 2, 6,-1,-1,-1,-1],
    [ 2, 7, 3, 2, 6, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 7,11, 6, 3, 8, 2, 8,10, 2, 8, 9,10,-1],
    [11, 6, 7,10, 0, 9,10, 2, 0,-1,-1,-1,-1],
    [ 2, 1,10, 7,11, 6, 8, 0, 3,-1,-1,-1,-1],
    [ 1,10, 2, 6, 7,11,-1,-1,-1,-1,-1,-1,-1],
    [ 7,11, 6, 3, 9, 1, 3, 8, 9,-1,-1,-1,-1],
    [ 9, 1, 0,11, 6, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 0, 3, 8,11, 6, 7,-1,-1,-1,-1,-1,-1,-1],
    [11, 6, 7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [11, 7, 6,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 0, 8, 3,11, 7, 6,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 0, 1,11, 7, 6,-1,-1,-1,-1,-1,-1,-1],
    [ 7, 6,11, 3, 1, 9, 3, 9, 8,-1,-1,-1,-1],
    [ 1, 2,10, 6,11, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 2,10, 1, 7, 6,11, 8, 3, 0,-1,-1,-1,-1],
    [11, 7, 6,10, 9, 0,10, 0, 2,-1,-1,-1,-1],
    [ 7, 6,11, 3, 2, 8, 8, 2,10, 8,10, 9,-1],
    [ 2, 3, 7, 2, 7, 6,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 7, 0, 7, 6, 0, 0, 6, 2,-1,-1,-1,-1],
    [ 1, 9, 0, 3, 7, 6, 3, 6, 2,-1,-1,-1,-1],
    [ 7, 6, 2, 7, 2, 9, 2, 1, 9, 7, 9, 8,-1],
    [ 6,10, 7,10, 1, 7, 7, 1, 3,-1,-1,-1,-1],
    [ 6,10, 1, 6, 1, 7, 7, 1, 0, 7, 0, 8,-1],
    [ 9, 0, 3, 6, 9, 3, 6,10, 9, 6, 3, 7,-1],
    [ 6,10, 7, 7,10, 8,10, 9, 8,-1,-1,-1,-1],
    [ 8, 4, 6, 8, 6,11,-1,-1,-1,-1,-1,-1,-1],
    [11, 3, 6, 3, 0, 6, 6, 0, 4,-1,-1,-1,-1],
    [ 0, 1, 9, 4, 6,11, 4,11, 8,-1,-1,-1,-1],
    [ 1, 9, 4,11, 1, 4,11, 3, 1,11, 4, 6,-1],
    [10, 1, 2,11, 8, 4,11, 4, 6,-1,-1,-1,-1],
    [10, 1, 2,11, 3, 6, 6, 3, 0, 6, 0, 4,-1],
    [ 0, 2,10, 0,10, 9, 4,11, 8, 4, 6,11,-1],
    [ 2,11, 3, 6, 9, 4, 6,10, 9,-1,-1,-1,-1],
    [ 3, 8, 2, 8, 4, 2, 2, 4, 6,-1,-1,-1,-1],
    [ 2, 0, 4, 2, 4, 6,-1,-1,-1,-1,-1,-1,-1],
    [ 1, 9, 0, 3, 8, 2, 2, 8, 4, 2, 4, 6,-1],
    [ 9, 4, 1, 1, 4, 2, 4, 6, 2,-1,-1,-1,-1],
    [ 8, 4, 6, 8, 6, 1, 6,10, 1, 8, 1, 3,-1],
    [ 1, 0,10,10, 0, 6, 0, 4, 6,-1,-1,-1,-1],
    [ 8, 0, 3, 9, 6,10, 9, 4, 6,-1,-1,-1,-1],
    [10, 4, 6,10, 9, 4,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 5, 4, 7, 6,11,-1,-1,-1,-1,-1,-1,-1],
    [ 4, 9, 5, 3, 0, 8,11, 7, 6,-1,-1,-1,-1],
    [ 6,11, 7, 4, 0, 1, 4, 1, 5,-1,-1,-1,-1],
    [ 6,11, 7, 4, 8, 5, 5, 8, 3, 5, 3, 1,-1],
    [ 6,11, 7, 1, 2,10, 9, 5, 4,-1,-1,-1,-1],
    [11, 7, 6, 8, 3, 0, 1, 2,10, 9, 5, 4,-1],
    [11, 7, 6,10, 5, 2, 2, 5, 4, 2, 4, 0,-1],
    [ 7, 4, 8, 2,11, 3,10, 5, 6,-1,-1,-1,-1],
    [ 4, 9, 5, 6, 2, 3, 6, 3, 7,-1,-1,-1,-1],
    [ 9, 5, 4, 8, 7, 0, 0, 7, 6, 0, 6, 2,-1],
    [ 4, 0, 1, 4, 1, 5, 6, 3, 7, 6, 2, 3,-1],
    [ 7, 4, 8, 5, 2, 1, 5, 6, 2,-1,-1,-1,-1],
    [ 4, 9, 5, 6,10, 7, 7,10, 1, 7, 1, 3,-1],
    [ 5, 6,10, 0, 9, 1, 8, 7, 4,-1,-1,-1,-1],
    [ 5, 6,10, 7, 0, 3, 7, 4, 0,-1,-1,-1,-1],
    [10, 5, 6, 4, 8, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 5, 6, 9, 6,11, 9, 9,11, 8,-1,-1,-1,-1],
    [ 0, 9, 5, 0, 5, 3, 3, 5, 6, 3, 6,11,-1],
    [ 0, 1, 5, 0, 5,11, 5, 6,11, 0,11, 8,-1],
    [11, 3, 6, 6, 3, 5, 3, 1, 5,-1,-1,-1,-1],
    [ 1, 2,10, 5, 6, 9, 9, 6,11, 9,11, 8,-1],
    [ 1, 0, 9, 6,10, 5,11, 3, 2,-1,-1,-1,-1],
    [ 6,10, 5, 2, 8, 0, 2,11, 8,-1,-1,-1,-1],
    [ 3, 2,11,10, 5, 6,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 5, 6, 3, 9, 6, 3, 8, 9, 3, 6, 2,-1],
    [ 5, 6, 9, 9, 6, 0, 6, 2, 0,-1,-1,-1,-1],
    [ 0, 3, 8, 2, 5, 6, 2, 1, 5,-1,-1,-1,-1],
    [ 1, 6, 2, 1, 5, 6,-1,-1,-1,-1,-1,-1,-1],
    [10, 5, 6, 9, 3, 8, 9, 1, 3,-1,-1,-1,-1],
    [ 0, 9, 1, 5, 6,10,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 0, 3,10, 5, 6,-1,-1,-1,-1,-1,-1,-1],
    [10, 5, 6,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [11, 7, 5,11, 5,10,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 0, 8, 7, 5,10, 7,10,11,-1,-1,-1,-1],
    [ 9, 0, 1,10,11, 7,10, 7, 5,-1,-1,-1,-1],
    [ 3, 1, 9, 3, 9, 8, 7,10,11, 7, 5,10,-1],
    [ 2,11, 1,11, 7, 1, 1, 7, 5,-1,-1,-1,-1],
    [ 0, 8, 3, 2,11, 1, 1,11, 7, 1, 7, 5,-1],
    [ 9, 0, 2, 9, 2, 7, 2,11, 7, 9, 7, 5,-1],
    [11, 3, 2, 8, 5, 9, 8, 7, 5,-1,-1,-1,-1],
    [10, 2, 5, 2, 3, 5, 5, 3, 7,-1,-1,-1,-1],
    [ 5,10, 2, 8, 5, 2, 8, 7, 5, 8, 2, 0,-1],
    [ 9, 0, 1,10, 2, 5, 5, 2, 3, 5, 3, 7,-1],
    [ 1,10, 2, 5, 8, 7, 5, 9, 8,-1,-1,-1,-1],
    [ 1, 3, 7, 1, 7, 5,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 7, 0, 0, 7, 1, 7, 5, 1,-1,-1,-1,-1],
    [ 0, 3, 9, 9, 3, 5, 3, 7, 5,-1,-1,-1,-1],
    [ 9, 7, 5, 9, 8, 7,-1,-1,-1,-1,-1,-1,-1],
    [ 4, 5, 8, 5,10, 8, 8,10,11,-1,-1,-1,-1],
    [ 3, 0, 4, 3, 4,10, 4, 5,10, 3,10,11,-1],
    [ 0, 1, 9, 4, 5, 8, 8, 5,10, 8,10,11,-1],
    [ 5, 9, 4, 1,11, 3, 1,10,11,-1,-1,-1,-1],
    [ 8, 4, 5, 2, 8, 5, 2,11, 8, 2, 5, 1,-1],
    [ 3, 2,11, 1, 4, 5, 1, 0, 4,-1,-1,-1,-1],
    [ 9, 4, 5, 8, 2,11, 8, 0, 2,-1,-1,-1,-1],
    [11, 3, 2, 9, 4, 5,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 8, 4, 3, 4, 2, 2, 4, 5, 2, 5,10,-1],
    [10, 2, 5, 5, 2, 4, 2, 0, 4,-1,-1,-1,-1],
    [ 0, 3, 8, 5, 9, 4,10, 2, 1,-1,-1,-1,-1],
    [ 2, 1,10, 9, 4, 5,-1,-1,-1,-1,-1,-1,-1],
    [ 4, 5, 8, 8, 5, 3, 5, 1, 3,-1,-1,-1,-1],
    [ 5, 0, 4, 5, 1, 0,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 8, 0, 4, 5, 9,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 4, 5,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 7, 4,11, 4, 9,11,11, 9,10,-1,-1,-1,-1],
    [ 3, 0, 8, 7, 4,11,11, 4, 9,11, 9,10,-1],
    [11, 7, 4, 1,11, 4, 1,10,11, 1, 4, 0,-1],
    [ 8, 7, 4,11, 1,10,11, 3, 1,-1,-1,-1,-1],
    [ 2,11, 7, 2, 7, 1, 1, 7, 4, 1, 4, 9,-1],
    [ 3, 2,11, 4, 8, 7, 9, 1, 0,-1,-1,-1,-1],
    [ 7, 4,11,11, 4, 2, 4, 0, 2,-1,-1,-1,-1],
    [ 2,11, 3, 7, 4, 8,-1,-1,-1,-1,-1,-1,-1],
    [ 2, 3, 7, 2, 7, 9, 7, 4, 9, 2, 9,10,-1],
    [ 4, 8, 7, 0,10, 2, 0, 9,10,-1,-1,-1,-1],
    [ 2, 1,10, 0, 7, 4, 0, 3, 7,-1,-1,-1,-1],
    [10, 2, 1, 8, 7, 4,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 1, 4, 4, 1, 7, 1, 3, 7,-1,-1,-1,-1],
    [ 1, 0, 9, 8, 7, 4,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 4, 0, 3, 7, 4,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 7, 4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 9,10, 8,10,11,-1,-1,-1,-1,-1,-1,-1],
    [ 0, 9, 3, 3, 9,11, 9,10,11,-1,-1,-1,-1],
    [ 1,10, 0, 0,10, 8,10,11, 8,-1,-1,-1,-1],
    [10, 3, 1,10,11, 3,-1,-1,-1,-1,-1,-1,-1],
    [ 2,11, 1, 1,11, 9,11, 8, 9,-1,-1,-1,-1],
    [11, 3, 2, 0, 9, 1,-1,-1,-1,-1,-1,-1,-1],
    [11, 0, 2,11, 8, 0,-1,-1,-1,-1,-1,-1,-1],
    [11, 3, 2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 3, 8, 2, 2, 8,10, 8, 9,10,-1,-1,-1,-1],
    [ 9, 2, 0, 9,10, 2,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 0, 3, 1,10, 2,-1,-1,-1,-1,-1,-1,-1],
    [10, 2, 1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 1, 3, 8, 9, 1,-1,-1,-1,-1,-1,-1,-1],
    [ 9, 1, 0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [ 8, 0, 3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
    [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]
];