mandelbulber2/src/marchingcubes.cpp

/**
 * Mandelbulber v2, a 3D fractal generator       ,=#MKNmMMKmmßMNWy,
 *                                             ,B" ]L,,p%%%,,,§;, "K
 * Copyright (C) 2016-21 Mandelbulber Team     §R-==%w["'~5]m%=L.=~5N
 *                                        ,=mm=§M ]=4 yJKA"/-Nsaj  "Bw,==,,
 * This file is part of Mandelbulber.    §R.r= jw",M  Km .mM  FW ",§=ß., ,TN
 *                                     ,4R =%["w[N=7]J '"5=],""]]M,w,-; T=]M
 * Mandelbulber is free software:     §R.ß~-Q/M=,=5"v"]=Qf,'§"M= =,M.§ Rz]M"Kw
 * you can redistribute it and/or     §w "xDY.J ' -"m=====WeC=\ ""%""y=%"]"" §
 * modify it under the terms of the    "§M=M =D=4"N #"%==A%p M§ M6  R' #"=~.4M
 * GNU General Public License as        §W =, ][T"]C  §  § '§ e===~ U  !§[Z ]N
 * published by the                    4M",,Jm=,"=e~  §  §  j]]""N  BmM"py=ßM
 * Free Software Foundation,          ]§ T,M=& 'YmMMpM9MMM%=w=,,=MT]M m§;'§,
 * either version 3 of the License,    TWw [.j"5=~N[=§%=%W,T ]R,"=="Y[LFT ]N
 * or (at your option)                   TW=,-#"%=;[  =Q:["V""  ],,M.m == ]N
 * any later version.                      J§"mr"] ,=,," =="""J]= M"M"]==ß"
 *                                          §= "=C=4 §"eM "=B:m|4"]#F,§~
 * Mandelbulber is distributed in            "9w=,,]w em%wJ '"~" ,=,,ß"
 * the hope that it will be useful,                 . "K=  ,=RMMMßM"""
 * but WITHOUT ANY WARRANTY;                            .'''
 * without even the implied warranty
 * of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 *
 * See the GNU General Public License for more details.
 * You should have received a copy of the GNU General Public License
 * along with Mandelbulber. If not, see <http://www.gnu.org/licenses/>.
 *
 * ###########################################################################
 *
 * Authors: pmneila, Sebastian Jennen (jenzebas@gmail.com)
 *
 * Re-licensed with the written authorization of P. M. Neila
 * for use with Mandelbulber. See here for original code:
 * https://github.com/pmneila/PyMCubes/
 */

#include "marchingcubes.h"

#include <QMap>

#include "calculate_distance.hpp"
#include "common_math.h"
#include "compute_fractal.hpp"
#include "fractal_container.hpp"
#include "fractparams.hpp"
#include "initparameters.hpp"
#include "nine_fractals.hpp"
#include "opencl_engine.h"
#include "opencl_engine_render_fractal.h"
#include "opencl_global.h"
#include "render_data.hpp"
#include "system_data.hpp"
#include "write_log.hpp"

// custom includes
#ifdef USE_OPENCL
#include "opencl/mesh_export_data_cl.h"
#endif

MarchingCubes::MarchingCubes(std::shared_ptr<const cParameterContainer> paramsContainer,
	std::shared_ptr<const cFractalContainer> fractalContainer, std::shared_ptr<sParamRender> params,
	std::shared_ptr<cNineFractals> fractals, std::shared_ptr<sRenderData> renderData, int numx,
	int numy, int numz, const CVector3 &lower, const CVector3 &upper, double dist_thresh, bool *stop,
	std::vector<double> &vertices, std::vector<long long> &polygons,
	std::vector<double> &colorIndices)
		: vertices{vertices}, polygons{polygons}, colorIndices{colorIndices}
{
	this->numx = numx;
	this->numy = numy;
	this->numz = numz;

	this->lower = lower;
	this->upper = upper;

	this->params = params;
	this->fractals = fractals;
	this->dist_thresh = dist_thresh;
	this->renderData = renderData;

	this->paramsContainer = paramsContainer;
	this->fractalContainer = fractalContainer;

	dx = (upper.x - lower.x) / numx;
	dy = (upper.y - lower.y) / numy;
	dz = (upper.z - lower.z) / numz;

	numyb = numy + 1;
	numzb = numz + 1;
	numyzb = numyb * numzb;
	z3 = numz * 3;
	yz3 = numy * z3;

	this->stop = stop;

	coloredMesh = paramsContainer->Get<bool>("mesh_color");

	try
	{
		shared_indices.resize(2LL * numy * numz * 3);
		voxelBuffer.resize(2LL * numyzb);
		colorBuffer.resize(2LL * numyzb);
	}
	catch (std::bad_alloc &ba)
	{
		FreeBuffers();
		throw ba;
	}
}

void MarchingCubes::FreeBuffers()
{
	shared_indices.clear();
	voxelBuffer.clear();
	colorBuffer.clear();
}

void MarchingCubes::RunMarchingCube()
{
	bool openClEnabled = false;
#ifdef USE_OPENCL

	openClEnabled =
		paramsContainer->Get<bool>("opencl_enabled")
		&& cOpenClEngineRenderFractal::enumClRenderEngineMode(paramsContainer->Get<int>("opencl_mode"))
				 != cOpenClEngineRenderFractal::clRenderEngineTypeNone;

	sClMeshExport clMeshParams;
	clMeshParams.distThresh = dist_thresh;
	clMeshParams.limitMax = toClFloat3(upper);
	clMeshParams.limitMin = toClFloat3(lower);
	clMeshParams.maxiter = params->N;
	clMeshParams.size = toClInt3(numx, numy, numz);
	clMeshParams.sliceHeight = numy + 1;
	clMeshParams.sliceWidth = numz + 1;
	clMeshParams.coloredMesh = coloredMesh;

	if (openClEnabled)
	{
		gOpenCl->openClEngineRenderFractal->Lock();
		gOpenCl->openClEngineRenderFractal->SetParameters(
			paramsContainer, fractalContainer, params, fractals, renderData, true);
		gOpenCl->openClEngineRenderFractal->SetMeshExportParameters(&clMeshParams);
		if (gOpenCl->openClEngineRenderFractal->LoadSourcesAndCompile(paramsContainer))
		{
			gOpenCl->openClEngineRenderFractal->CreateKernel4Program(paramsContainer);
			WriteLogDouble("OpenCl render fractal - needed mem:",
				gOpenCl->openClEngineRenderFractal->CalcNeededMemory() / 1048576.0, 2);
			gOpenCl->openClEngineRenderFractal->PreAllocateBuffers(paramsContainer);
			gOpenCl->openClEngineRenderFractal->CreateCommandQueue();
		}
		else
		{
			emit finished();
			gOpenCl->openClEngineRenderFractal->ReleaseMemory();
			gOpenCl->openClEngineRenderFractal->Unlock();
			return;
		}
	}

#endif // USE_OPENCL

	// numx, numy and numz are the numbers of evaluations in each direction
	for (long long i = 0; i < numx; ++i)
	{
		emit signalUpdateProgressAndStatus(i, polygons.size() / 3);

		// shift voxel planes
		if (i > 0)
		{
			for (long long jk = 0; jk < numyzb; ++jk)
			{
				long long ptr = jk;
				long long ptr2 = ptr + numyzb;
				voxelBuffer[ptr] = voxelBuffer[ptr2];
				colorBuffer[ptr] = colorBuffer[ptr2];
			}
		}

#ifdef USE_OPENCL
		if (openClEnabled)
		{
			size_t dataOffset = clMeshParams.sliceHeight * clMeshParams.sliceWidth;
			bool result = gOpenCl->openClEngineRenderFractal->Render(&voxelBuffer, &colorBuffer, nullptr,
				i, renderData->stopRequest, renderData.get(), dataOffset);

			if (!result)
			{
				gOpenCl->openClEngineRenderFractal->ReleaseMemory();
				gOpenCl->openClEngineRenderFractal->Unlock();
				return;
			}
		}
#endif // USE_OPENCL

		if (!openClEnabled)
		{
			calculateVoxelPlane(i);
		}
		if (i > 0)
		{
			calculateEdges(i);
		}
		if (*stop || systemData.globalStopRequest) break;
	}

#ifdef USE_OPENCL
	if (openClEnabled)
	{
		gOpenCl->openClEngineRenderFractal->ReleaseMemory();
		gOpenCl->openClEngineRenderFractal->Unlock();
	}
#endif // USE_OPENCL

	emit finished();
}

void MarchingCubes::calculateVoxelPlane(int i)
{
	// calculate voxel plane
	long long start = (i == 0) ? 0 : 1;
	for (long long ii = start; ii < 2; ++ii)
	{
		double xx = lower.x + dx * (ii + i);

		for (long long jj = 0; jj < numyb; ++jj)
		{
			if (*stop)
			{
				return;
			}

			double yy = lower.y + dy * jj;

#ifdef USE_OFFLOAD
#pragma offload target(mic) inout(voxelBuffer) inout(colorBuffer) nocopy(f)
#endif // USE_OFFLOAD

#pragma omp parallel for schedule(dynamic, 1)
			for (long long kk = 0; kk < numzb;
					 ++kk) // long long is used because size_t doesn't work with msvc and OpenMP
			{
				long long ptr = ii * numyzb + jj * numzb + kk;

				double zz = lower.z + dz * kk;
				voxelBuffer[ptr] = getDistance(xx, yy, zz, &colorBuffer[ptr]);
			}
		}
	}
}

void MarchingCubes::calculateEdges(int i)
{
	double x = lower.x + dx * i;
	double x_dx = lower.x + dx * (i + 1);
	const int i_mod_2 = i % 2;
	const int i_mod_2_inv = (i_mod_2 ? 0 : 1);

	for (long long j = 0; j < numy; ++j)
	{
		if (*stop)
		{
			return;
		}

		double y = lower.y + dy * j;
		double y_dy = lower.y + dy * (j + 1);

		for (long long k = 0; k < numz; ++k)
		{
			double z = lower.z + dz * k;
			double z_dz = lower.z + dz * (k + 1);

			double v[8];
			double colorIndex[8];
			v[0] = voxelBuffer[j * numzb + k];
			v[1] = voxelBuffer[numyzb + j * numzb + k];
			v[2] = voxelBuffer[numyzb + (j + 1) * numzb + k];
			v[3] = voxelBuffer[(j + 1) * numzb + k];
			v[4] = voxelBuffer[j * numzb + k + 1];
			v[5] = voxelBuffer[numyzb + j * numzb + k + 1];
			v[6] = voxelBuffer[numyzb + (j + 1) * numzb + k + 1];
			v[7] = voxelBuffer[(j + 1) * numzb + k + 1];

			colorIndex[0] = colorBuffer[j * numzb + k];
			colorIndex[1] = colorBuffer[numyzb + j * numzb + k];
			colorIndex[2] = colorBuffer[numyzb + (j + 1) * numzb + k];
			colorIndex[3] = colorBuffer[(j + 1) * numzb + k];
			colorIndex[4] = colorBuffer[j * numzb + k + 1];
			colorIndex[5] = colorBuffer[numyzb + j * numzb + k + 1];
			colorIndex[6] = colorBuffer[numyzb + (j + 1) * numzb + k + 1];
			colorIndex[7] = colorBuffer[(j + 1) * numzb + k + 1];

			unsigned int cubeindex = 0;

			for (int m = 0; m < 8; ++m)
				if (v[m] < dist_thresh) cubeindex |= 1 << m;

			// Generate vertices AVOIDING DUPLICATES.

			int edges = edge_table[cubeindex];
			std::vector<long long> indices(12, -1);
			if (edges & 0x040)
			{
				indices[6] = vertices.size() / 3;
				shared_indices[i_mod_2 * yz3 + j * z3 + k * 3 + 0] = indices[6];
				mc_add_vertex(x_dx, y_dy, z_dz, x, 0, v[6], v[7], dist_thresh, &vertices, colorIndex[6],
					colorIndex[7], &colorIndices);
			}
			if (edges & 0x020)
			{
				indices[5] = vertices.size() / 3;
				shared_indices[i_mod_2 * yz3 + j * z3 + k * 3 + 1] = indices[5];
				mc_add_vertex(x_dx, y, z_dz, y_dy, 1, v[5], v[6], dist_thresh, &vertices, colorIndex[5],
					colorIndex[6], &colorIndices);
			}
			if (edges & 0x400)
			{
				indices[10] = vertices.size() / 3;
				shared_indices[i_mod_2 * yz3 + j * z3 + k * 3 + 2] = indices[10];
				mc_add_vertex(x_dx, y + dx, z, z_dz, 2, v[2], v[6], dist_thresh, &vertices, colorIndex[2],
					colorIndex[6], &colorIndices);
			}

			if (edges & 0x001)
			{
				if (j == 0 || k == 0)
				{
					indices[0] = vertices.size() / 3;
					mc_add_vertex(x, y, z, x_dx, 0, v[0], v[1], dist_thresh, &vertices, colorIndex[0],
						colorIndex[1], &colorIndices);
				}
				else
					indices[0] = shared_indices[i_mod_2 * yz3 + (j - 1) * z3 + (k - 1) * 3 + 0];
			}
			if (edges & 0x002)
			{
				if (k == 0)
				{
					indices[1] = vertices.size() / 3;
					mc_add_vertex(x_dx, y, z, y_dy, 1, v[1], v[2], dist_thresh, &vertices, colorIndex[1],
						colorIndex[2], &colorIndices);
				}
				else
					indices[1] = shared_indices[i_mod_2 * yz3 + j * z3 + (k - 1) * 3 + 1];
			}
			if (edges & 0x004)
			{
				if (k == 0)
				{
					indices[2] = vertices.size() / 3;
					mc_add_vertex(x_dx, y_dy, z, x, 0, v[2], v[3], dist_thresh, &vertices, colorIndex[2],
						colorIndex[3], &colorIndices);
				}
				else
					indices[2] = shared_indices[i_mod_2 * yz3 + j * z3 + (k - 1) * 3 + 0];
			}
			if (edges & 0x008)
			{
				if (i == 0 || k == 0)
				{
					indices[3] = vertices.size() / 3;
					mc_add_vertex(x, y_dy, z, y, 1, v[3], v[0], dist_thresh, &vertices, colorIndex[3],
						colorIndex[0], &colorIndices);
				}
				else
					indices[3] = shared_indices[i_mod_2_inv * yz3 + j * z3 + (k - 1) * 3 + 1];
			}
			if (edges & 0x010)
			{
				if (j == 0)
				{
					indices[4] = vertices.size() / 3;
					mc_add_vertex(x, y, z_dz, x_dx, 0, v[4], v[5], dist_thresh, &vertices, colorIndex[4],
						colorIndex[5], &colorIndices);
				}
				else
					indices[4] = shared_indices[i_mod_2 * yz3 + (j - 1) * z3 + k * 3 + 0];
			}
			if (edges & 0x080)
			{
				if (i == 0)
				{
					indices[7] = vertices.size() / 3;
					mc_add_vertex(x, y_dy, z_dz, y, 1, v[7], v[4], dist_thresh, &vertices, colorIndex[7],
						colorIndex[4], &colorIndices);
				}
				else
					indices[7] = shared_indices[i_mod_2_inv * yz3 + j * z3 + k * 3 + 1];
			}
			if (edges & 0x100)
			{
				if (i == 0 || j == 0)
				{
					indices[8] = vertices.size() / 3;
					mc_add_vertex(x, y, z, z_dz, 2, v[0], v[4], dist_thresh, &vertices, colorIndex[0],
						colorIndex[4], &colorIndices);
				}
				else
					indices[8] = shared_indices[i_mod_2_inv * yz3 + (j - 1) * z3 + k * 3 + 2];
			}
			if (edges & 0x200)
			{
				if (j == 0)
				{
					indices[9] = vertices.size() / 3;
					mc_add_vertex(x_dx, y, z, z_dz, 2, v[1], v[5], dist_thresh, &vertices, colorIndex[1],
						colorIndex[3], &colorIndices);
				}
				else
					indices[9] = shared_indices[i_mod_2 * yz3 + (j - 1) * z3 + k * 3 + 2];
			}
			if (edges & 0x800)
			{
				if (i == 0)
				{
					indices[11] = vertices.size() / 3;
					mc_add_vertex(x, y_dy, z, z_dz, 2, v[3], v[7], dist_thresh, &vertices, colorIndex[3],
						colorIndex[7], &colorIndices);
				}
				else
					indices[11] = shared_indices[i_mod_2_inv * yz3 + j * z3 + k * 3 + 2];
			}

			int tri;
			int *triangle_table_ptr = triangle_table[cubeindex];
			for (int m = 0; tri = triangle_table_ptr[m], tri != -1; ++m)
				polygons.push_back(indices[tri]);
		}
	}
}

#ifdef USE_OFFLOAD
__declspec(target(mic))
#endif // USE_OFFLOAD
	double MarchingCubes::getDistance(double x, double y, double z, double *colorIndex) const
{
	CVector3 point;
	point.x = x;
	point.y = y;
	point.z = z;

	sDistanceOut distanceOut;
	sDistanceIn distanceIn(point, dist_thresh, false);

	double dist =
		CalculateDistance(*params.get(), *fractals.get(), distanceIn, &distanceOut, renderData.get());

	cObjectData objectData = renderData->objectData[distanceOut.objectId];
	cMaterial *material = &renderData->materials[objectData.materialId];

	sFractalIn fractIn(point, params->minN, params->N, &params->common, -1, false, material);
	sFractalOut fractOut;

	Compute<fractal::calcModeColouring>(*fractals, fractIn, &fractOut);

	*colorIndex = fractOut.colorIndex;

	return dist;
}

int MarchingCubes::edge_table[256] = {0x000, 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c, 0x80c,
	0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00, 0x190, 0x099, 0x393, 0x29a, 0x596, 0x49f, 0x795,
	0x69c, 0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90, 0x230, 0x339, 0x033, 0x13a, 0x636,
	0x73f, 0x435, 0x53c, 0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30, 0x3a0, 0x2a9, 0x1a3,
	0x0aa, 0x7a6, 0x6af, 0x5a5, 0x4ac, 0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0, 0x460,
	0x569, 0x663, 0x76a, 0x066, 0x16f, 0x265, 0x36c, 0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69,
	0xb60, 0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0x0ff, 0x3f5, 0x2fc, 0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa,
	0x8f3, 0xbf9, 0xaf0, 0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x055, 0x15c, 0xe5c, 0xf55, 0xc5f,
	0xd56, 0xa5a, 0xb53, 0x859, 0x950, 0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0x0cc, 0xfcc,
	0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0, 0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5,
	0xfcc, 0x0cc, 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0, 0x950, 0x859, 0xb53, 0xa5a, 0xd56,
	0xc5f, 0xf55, 0xe5c, 0x15c, 0x055, 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650, 0xaf0, 0xbf9, 0x8f3,
	0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc, 0x2fc, 0x3f5, 0x0ff, 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0, 0xb60,
	0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c, 0x36c, 0x265, 0x16f, 0x066, 0x76a, 0x663, 0x569,
	0x460, 0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac, 0x4ac, 0x5a5, 0x6af, 0x7a6, 0x0aa,
	0x1a3, 0x2a9, 0x3a0, 0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c, 0x53c, 0x435, 0x73f,
	0x636, 0x13a, 0x033, 0x339, 0x230, 0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c, 0x69c,
	0x795, 0x49f, 0x596, 0x29a, 0x393, 0x099, 0x190, 0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905,
	0x80c, 0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x000};

int MarchingCubes::triangle_table[256][16] = {
	{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1},
	{3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1},
	{3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1},
	{3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1},
	{9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1},
	{9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
	{2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1},
	{8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1},
	{9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
	{4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1},
	{3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1},
	{1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1},
	{4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1},
	{4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1},
	{9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
	{5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1},
	{2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1},
	{9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
	{0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
	{2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1},
	{10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1},
	{4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1},
	{5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1},
	{5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1},
	{9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1},
	{0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1},
	{1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1},
	{10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1},
	{8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1},
	{2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1},
	{7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1},
	{9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1},
	{2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1},
	{11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1},
	{9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1},
	{5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1},
	{11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1},
	{11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
	{1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1},
	{9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1},
	{5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1},
	{2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
	{0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
	{5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1},
	{6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1},
	{3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1},
	{6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1},
	{5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1},
	{1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
	{10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1},
	{6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1},
	{8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1},
	{7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1},
	{3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
	{5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1},
	{0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1},
	{9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1},
	{8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1},
	{5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1},
	{0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1},
	{6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1},
	{10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1},
	{10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1},
	{8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1},
	{1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1},
	{3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1},
	{0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1},
	{10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1},
	{3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1},
	{6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1},
	{9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1},
	{8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1},
	{3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1},
	{6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1},
	{0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1},
	{10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1},
	{10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1},
	{2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1},
	{7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1},
	{7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1},
	{2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1},
	{1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1},
	{11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1},
	{8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1},
	{0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1},
	{7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
	{10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
	{2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
	{6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1},
	{7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1},
	{2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1},
	{1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1},
	{10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1},
	{10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1},
	{0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1},
	{7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1},
	{6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1},
	{8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1},
	{9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1},
	{6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1},
	{4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1},
	{10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1},
	{8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1},
	{0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1},
	{1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1},
	{8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1},
	{10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1},
	{4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1},
	{10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
	{5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
	{11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1},
	{9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
	{6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1},
	{7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1},
	{3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1},
	{7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1},
	{9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1},
	{3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1},
	{6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1},
	{9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1},
	{1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1},
	{4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1},
	{7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1},
	{6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1},
	{3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1},
	{0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1},
	{6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1},
	{0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1},
	{11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1},
	{6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1},
	{5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1},
	{9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1},
	{1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1},
	{1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1},
	{10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1},
	{0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1},
	{5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1},
	{10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1},
	{11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1},
	{9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1},
	{7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1},
	{2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1},
	{8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1},
	{9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1},
	{9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1},
	{1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1},
	{9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1},
	{9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1},
	{5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1},
	{0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1},
	{10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1},
	{2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1},
	{0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1},
	{0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1},
	{9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1},
	{5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1},
	{3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1},
	{5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1},
	{8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1},
	{0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1},
	{9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1},
	{0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1},
	{1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1},
	{3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1},
	{4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1},
	{9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1},
	{11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1},
	{11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1},
	{2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1},
	{9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1},
	{3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1},
	{1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1},
	{4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1},
	{4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1},
	{0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1},
	{3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1},
	{3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1},
	{0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1},
	{9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1},
	{1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
	{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}};