LLVM Proto Fuzzer - Run Functions on Suite of Inputs

[emmettneyman]

Summary

Added corpus of arrays to use as inputs for the functions. Check that the two
functions modify the inputted arrays in the same way.

[morehouse]

clang/tools/clang-fuzzer/handle-llvm/handle_llvm.cpp

173 ↗

(On Diff #158782)

Why do we need to copy the function somewhere else? Looks very error-prone and unnecessary. Also makes this patch larger than it needs to be.

clang/tools/clang-fuzzer/handle-llvm/input_arrays.cpp

30 ↗

(On Diff #158782)

Do the generated functions ever modify arrays a and b, or just c? If just c, we can avoid lots of memcpys here.

clang/tools/clang-fuzzer/handle-llvm/input_arrays.h

34 ↗

(On Diff #158782)

Use the constants you just defined.

[emmettneyman]

clang/tools/clang-fuzzer/handle-llvm/handle_llvm.cpp

173 ↗

(On Diff #158782)

I'm copying the functions because otherwise, the generated machine code gets lost as soon as we exit that function's scope. So I'd have to run the functions inside CreateJITFunction if I don't copy it.

I thought about doing it this way: moving the code from RunFuncsOnInputs to the bottom of CreateJITFunction and then comparing the arrays after both calls to CreateJITFunction inside HandleLLVM. Do you think that would be cleaner?

clang/tools/clang-fuzzer/handle-llvm/input_arrays.cpp

30 ↗

(On Diff #158782)

Right now the generated functions can modify any of the arrays.

[emmettneyman]

Replaced hardcoded numbers with variables

[morehouse]

clang/tools/clang-fuzzer/handle-llvm/handle_llvm.cpp

173 ↗

(On Diff #158782)

Or just increase the scope of EE.

[emmettneyman]

clang/tools/clang-fuzzer/handle-llvm/handle_llvm.cpp

173 ↗

(On Diff #158782)

When I tried to increase the scope of EE (and also M since EntryFunc lives inside the module), the program segfaulted immediately after exiting CreateJITFunc, I think while trying to deconstruct an object from the function. I'm not sure if there's a way around this since there are so many objects being created inside CreateJITFunc. But it's definitely possible I'm missing something with how unique_ptr work.

[emmettneyman]

An unrelated question:
Right now I have a mix of static and non-static functions in handle_llvm.cpp. Should they all be static?

[emmettneyman]

Refactored code to avoid memcpy-ing function

[kcc]

clang/tools/clang-fuzzer/handle-llvm/handle_llvm.cpp

128 ↗

(On Diff #159083)

looks like code duplication, also strange name for a variable: 'x'.
Can't we just have one loop here and pass OptArrays/UnoptArrays as the parameter?

clang/tools/clang-fuzzer/handle-llvm/input_arrays.h

36 ↗

(On Diff #159083)

constants are not diverse enough.

[morehouse]

clang/tools/clang-fuzzer/handle-llvm/handle_llvm.cpp

75 ↗

(On Diff #159083)

Unnecessary comment. The naming and implementation of this function are intuitive.

170 ↗

(On Diff #159083)

Does reinterpret_cast work here?

184 ↗

(On Diff #159083)

The size here is reused a few times. Let's create a variable for it.

[morehouse]

In D50194#1187756, @emmettneyman wrote:

An unrelated question:
Right now I have a mix of static and non-static functions in handle_llvm.cpp. Should they all be static?

Any functions that are only used in the same file can and should be static or in an unnamed namespace. Functions that implement something from a header file must not be static.

[emmettneyman]

clang/tools/clang-fuzzer/handle-llvm/input_arrays.h

36 ↗

(On Diff #159083)

Yeah, I will completely redo the input arrays.

[emmettneyman]

Added static to some functions, made small fixes

[morehouse]

clang/tools/clang-fuzzer/handle-llvm/handle_llvm.cpp

132 ↗

(On Diff #159100)

CreateAndRunJITFunc describes this better.

clang/tools/clang-fuzzer/handle-llvm/input_arrays.h

15 ↗

(On Diff #159100)

Are these includes needed?

19 ↗

(On Diff #159100)

Maybe prefix these names with k since they are constant.

36 ↗

(On Diff #159083)

Please land today once you do.

[emmettneyman]

New input arrays and minor fixes

[emmettneyman]

ready to land

tools/clang-fuzzer/handle-llvm/handle_llvm.h

 #ifndef LLVM_CLANG_TOOLS_CLANG_FUZZER_HANDLE_LLVM_HANDLELLVM_H
 #define LLVM_CLANG_TOOLS_CLANG_FUZZER_HANDLE_LLVM_HANDLELLVM_H
 
 #include <string>
 #include <vector>
 
 namespace clang_fuzzer {
 void HandleLLVM(const std::string &S,
                 const std::vector<const char *> &ExtraArgs);
 } // namespace clang_fuzzer
 
 #endif

tools/clang-fuzzer/handle-llvm/handle_llvm.cpp

 // Implements HandleLLVM for use by the Clang fuzzers. First runs a loop
 // vectorizer optimization pass over the given IR code. Then mimics lli on both
 // versions to JIT the generated code and execute it. Currently, functions are 
 // executed on dummy inputs.
 //
 //===----------------------------------------------------------------------===//
 
 #include "handle_llvm.h"
+#include "input_arrays.h"
 
 #include "llvm/ADT/Triple.h"
 #include "llvm/Analysis/TargetLibraryInfo.h"
 #include "llvm/Analysis/TargetTransformInfo.h"
 #include "llvm/CodeGen/CommandFlags.inc"
 #include "llvm/CodeGen/MachineModuleInfo.h"
 #include "llvm/CodeGen/TargetPassConfig.h"
 #include "llvm/ExecutionEngine/JITEventListener.h"

 #include "llvm/Support/TargetSelect.h"
 #include "llvm/Target/TargetMachine.h"
 #include "llvm/Transforms/IPO/PassManagerBuilder.h"
 #include "llvm/Transforms/IPO.h"
 #include "llvm/Transforms/Vectorize.h"
 
 using namespace llvm;
 
+// Define a type for the functions that are compiled and executed
+typedef void (*LLVMFunc)(int*, int*, int*, int);
+
 // Helper function to parse command line args and find the optimization level
 static void getOptLevel(const std::vector<const char *> &ExtraArgs,
                               CodeGenOpt::Level &OLvl) {
   // Find the optimization level from the command line args
   OLvl = CodeGenOpt::Default;
   for (auto &A : ExtraArgs) {
     if (A[0] == '-' && A[1] == 'O') {
       switch(A[2]) {
         case '0': OLvl = CodeGenOpt::None; break;
         case '1': OLvl = CodeGenOpt::Less; break;
         case '2': OLvl = CodeGenOpt::Default; break;
         case '3': OLvl = CodeGenOpt::Aggressive; break;
         default:
           errs() << "error: opt level must be between 0 and 3.\n";
           std::exit(1);
       }
     }
   }
 }
 
-void ErrorAndExit(std::string message) {
+static void ErrorAndExit(std::string message) {
   errs()<< "ERROR: " << message << "\n";
   std::exit(1);
 }
 
 // Helper function to add optimization passes to the TargetMachine at the 
 // specified optimization level, OptLevel
 static void AddOptimizationPasses(legacy::PassManagerBase &MPM,
                                   CodeGenOpt::Level OptLevel,
                                   unsigned SizeLevel) {
   // Create and initialize a PassManagerBuilder
   PassManagerBuilder Builder;
   Builder.OptLevel = OptLevel;
   Builder.SizeLevel = SizeLevel;
   Builder.Inliner = createFunctionInliningPass(OptLevel, SizeLevel, false);
   Builder.LoopVectorize = true;
   Builder.populateModulePassManager(MPM);
 }
 
 // Mimics the opt tool to run an optimization pass over the provided IR
-std::string OptLLVM(const std::string &IR, CodeGenOpt::Level OLvl) {
+static std::string OptLLVM(const std::string &IR, CodeGenOpt::Level OLvl) {
   // Create a module that will run the optimization passes
   SMDiagnostic Err;
   LLVMContext Context;
   std::unique_ptr<Module> M = parseIR(MemoryBufferRef(IR, "IR"), Err, Context);
   if (!M || verifyModule(*M, &errs()))
     ErrorAndExit("Could not parse IR");
 
   setFunctionAttributes(getCPUStr(), getFeaturesStr(), *M);
static std::string OptLLVM(const std::string &IR, CodeGenOpt::Level OLvl) {
   raw_string_ostream OS(outString);
   Passes.add(createPrintModulePass(OS, "", false));
 
   Passes.run(*M);
 
   return OS.str();
 }
 
-void CreateAndRunJITFun(const std::string &IR, CodeGenOpt::Level OLvl) {
+// Takes a function and runs it on a set of inputs
+// First determines whether f is the optimized or unoptimized function
+static void RunFuncOnInputs(LLVMFunc f, int Arr[kNumArrays][kArraySize]) {
+  for (int i = 0; i < kNumArrays / 3; i++)
+    f(Arr[i], Arr[i + (kNumArrays / 3)], Arr[i + (2 * kNumArrays / 3)],
+      kArraySize);
+}
+
+// Takes a string of IR and compiles it using LLVM's JIT Engine
+static void CreateAndRunJITFunc(const std::string &IR, CodeGenOpt::Level OLvl) {
   SMDiagnostic Err;
   LLVMContext Context;
-  std::unique_ptr<Module> M = parseIR(MemoryBufferRef(IR, "IR"), Err,
-                                          Context);
+  std::unique_ptr<Module> M = parseIR(MemoryBufferRef(IR, "IR"), Err, Context);
   if (!M)
     ErrorAndExit("Could not parse IR");
 
   Function *EntryFunc = M->getFunction("foo");
   if (!EntryFunc)
     ErrorAndExit("Function not found in module");
 
   std::string ErrorMsg;

 //   warning: ISO C++ forbids casting between pointer-to-function and
 //   pointer-to-object [-Wpedantic]
 //
 // Since C++11 this casting is conditionally supported and GCC versions
 // starting from 4.9.0 don't warn about the cast.
 #pragma GCC diagnostic push
 #pragma GCC diagnostic ignored "-Wpedantic"
 #endif
-  func f = reinterpret_cast<func>(EE->getPointerToFunction(EntryFunc));
+  LLVMFunc f = reinterpret_cast<LLVMFunc>(EE->getPointerToFunction(EntryFunc)); 
 #if defined(__GNUC__) && !defined(__clang) &&                                  \
     ((__GNUC__ == 4) && (__GNUC_MINOR__ < 9))
 #pragma GCC diagnostic pop
 #endif
 
-  // Define some dummy arrays to use an input for now
-  int a[] = {1};
-  int b[] = {1};
-  int c[] = {1};
-  f(a, b, c, 1);
+  // Figure out if we are running the optimized func or the unoptimized func
+  RunFuncOnInputs(f, (OLvl == CodeGenOpt::None) ? UnoptArrays : OptArrays);
 
   EE->runStaticConstructorsDestructors(true);
 }
 
 // Main fuzz target called by ExampleClangLLVMProtoFuzzer.cpp
 // Mimics the lli tool to JIT the LLVM IR code and execute it
 void clang_fuzzer::HandleLLVM(const std::string &IR,
                               const std::vector<const char *> &ExtraArgs) {
+  // Populate OptArrays and UnoptArrays with the arrays from InputArrays
+  memcpy(OptArrays, InputArrays, kTotalSize);
+  memcpy(UnoptArrays, InputArrays, kTotalSize);
+
   // Parse ExtraArgs to set the optimization level
   CodeGenOpt::Level OLvl;
   getOptLevel(ExtraArgs, OLvl);
 
   // First we optimize the IR by running a loop vectorizer pass
   std::string OptIR = OptLLVM(IR, OLvl);
 
-  CreateAndRunJITFun(OptIR, OLvl);
-  CreateAndRunJITFun(IR, CodeGenOpt::None);
-  
+  CreateAndRunJITFunc(OptIR, OLvl);
+  CreateAndRunJITFunc(IR, CodeGenOpt::None);
+
+  if (memcmp(OptArrays, UnoptArrays, kTotalSize))
+    ErrorAndExit("!!!BUG!!!");
   return;
 }

tools/clang-fuzzer/handle-llvm/input_arrays.h

+//==-- input_arrays.h - Helper function for LLVM fuzzer inputs -------------==//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// Define a few static variables used by the LLVM Proto Fuzzer
+//
+//===----------------------------------------------------------------------===//
+
+#include <climits>
+
+static const int kArraySize = 64;
+static const int kNumArrays = 93;
+static const int kTotalSize = sizeof(int) * kArraySize * kNumArrays;
+
+// Define two arrays that will hold the input and output for the two functions
+static int OptArrays[kNumArrays][kArraySize];
+static int UnoptArrays[kNumArrays][kArraySize];
+
+// Define a corpus of possible inputs
+static int InputArrays[kNumArrays][kArraySize] =
+{ {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {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, 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, 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, -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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+  {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {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, 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, 1, 1, 1, 1, 1, 1},
+  {INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX},
+  {INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN},
+  {-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, -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, -1, -1, -1, -1, -1, -1},
+  {16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16},
+  {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},
+  {1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024},
+  {65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535},
+  {-1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023},
+  {INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX},
+  {0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, },
+  {1, 1, 0, 3, 2, 5, 6, 2, 6, 3, 0, 19, 18, 17, 16, 0, 13, 11, 9, 7, 5, 3, 1, -3000, -3000, -3000, -3000, -3000, -3000, -3000, 0, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000},
+  {1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824},
+  {1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0},
+  {0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, },
+  {-0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0},
+  {1, 1, 2, 1, 6, 9, 10, 7, 2, 10, 4, 11, 10, 11, 0, 19, 26, 18, 10, 2, 14, 7, 0, 39, 34, 29, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91},
+  {0, 0, 2, 0, 0, 1, 6, 9, 4, 12, 6, 13, 12, 0, 2, 21, 28, 20, 12, 4, 16, 9, 2, 41, 36, 31, 26, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93},
+  {1, 1, 0, 2, 2, 3, 8, 11, 6, 14, 8, 15, 14, 2, 4, 23, 30, 22, 14, 6, 18, 11, 4, 43, 38, 33, 28, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95},
+  {0, 0, 0, 4, 0, 0, 10, 13, 0, 16, 0, 17, 16, 4, 6, 25, 16, 24, 16, 8, 0, 13, 6, 45, 40, 35, 30, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97},
+  {1, 1, 2, 3, 2, 2, 0, 1, 2, 9, 2, 19, 18, 6, 8, 27, 18, 26, 18, 10, 2, 15, 8, 1, 42, 37, 32, 27, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 107, 106, 105, 104, 103, 102, 101, 100, 99},
+  {0, 0, 2, 5, 4, 4, 2, 3, 4, 11, 4, 21, 20, 8, 10, 29, 20, 28, 20, 12, 4, 17, 10, 3, 44, 39, 34, 29, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 109, 108, 107, 106, 105, 104, 103, 102, 101},
+  {1, 1, 0, 1, 6, 6, 4, 5, 6, 13, 6, 1, 22, 10, 12, 1, 22, 30, 22, 14, 6, 19, 12, 5, 46, 41, 36, 31, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 110, 109, 108, 107, 106, 105, 104, 103},
+  {0, 0, 0, 0, 4, 8, 0, 0, 8, 15, 8, 3, 12, 12, 0, 3, 24, 32, 24, 16, 8, 0, 14, 7, 0, 43, 38, 33, 28, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 111, 110, 109, 108, 107, 106, 105},
+  {1, 1, 2, 2, 6, 5, 2, 2, 10, 17, 10, 5, 14, 14, 2, 5, 26, 17, 26, 18, 10, 2, 16, 9, 2, 45, 40, 35, 30, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 113, 112, 111, 110, 109, 108, 107},
+  {0, 0, 2, 4, 0, 7, 4, 4, 12, 1, 12, 7, 16, 16, 4, 7, 28, 19, 28, 20, 12, 4, 18, 11, 4, 47, 42, 37, 32, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 114, 113, 112, 111, 110, 109},
+  {1, 1, 0, 3, 2, 9, 6, 6, 14, 3, 14, 9, 18, 18, 6, 9, 30, 21, 30, 22, 14, 6, 20, 13, 6, 49, 44, 39, 34, 29, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 115, 114, 113, 112, 111},
+  {1, 1, 0, 3, 2, 5, 6, 2, 6, 3, 0, 19, 18, 17, 16, 0, 13, 11, 9, 7, 5, 3, 1, -3000, -3000, -3000, -3000, -3000, -3000, -3000, 0, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000},
+  {1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824},
+  {1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0},
+  {0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, },
+  {-0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0},
+  {1, 1, 2, 1, 6, 9, 10, 7, 2, 10, 4, 11, 10, 11, 0, 19, 26, 18, 10, 2, 14, 7, 0, 39, 34, 29, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91},
+  {0, 0, 2, 0, 0, 1, 6, 9, 4, 12, 6, 13, 12, 0, 2, 21, 28, 20, 12, 4, 16, 9, 2, 41, 36, 31, 26, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93},
+  {1, 1, 0, 2, 2, 3, 8, 11, 6, 14, 8, 15, 14, 2, 4, 23, 30, 22, 14, 6, 18, 11, 4, 43, 38, 33, 28, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95},
+  {0, 0, 0, 4, 0, 0, 10, 13, 0, 16, 0, 17, 16, 4, 6, 25, 16, 24, 16, 8, 0, 13, 6, 45, 40, 35, 30, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97},
+  {1, 1, 2, 3, 2, 2, 0, 1, 2, 9, 2, 19, 18, 6, 8, 27, 18, 26, 18, 10, 2, 15, 8, 1, 42, 37, 32, 27, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 107, 106, 105, 104, 103, 102, 101, 100, 99},
+  {0, 0, 2, 5, 4, 4, 2, 3, 4, 11, 4, 21, 20, 8, 10, 29, 20, 28, 20, 12, 4, 17, 10, 3, 44, 39, 34, 29, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 109, 108, 107, 106, 105, 104, 103, 102, 101},
+  {1, 1, 0, 1, 6, 6, 4, 5, 6, 13, 6, 1, 22, 10, 12, 1, 22, 30, 22, 14, 6, 19, 12, 5, 46, 41, 36, 31, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 110, 109, 108, 107, 106, 105, 104, 103},
+  {0, 0, 0, 0, 4, 8, 0, 0, 8, 15, 8, 3, 12, 12, 0, 3, 24, 32, 24, 16, 8, 0, 14, 7, 0, 43, 38, 33, 28, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 111, 110, 109, 108, 107, 106, 105},
+  {1, 1, 2, 2, 6, 5, 2, 2, 10, 17, 10, 5, 14, 14, 2, 5, 26, 17, 26, 18, 10, 2, 16, 9, 2, 45, 40, 35, 30, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 113, 112, 111, 110, 109, 108, 107},
+  {0, 0, 2, 4, 0, 7, 4, 4, 12, 1, 12, 7, 16, 16, 4, 7, 28, 19, 28, 20, 12, 4, 18, 11, 4, 47, 42, 37, 32, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 114, 113, 112, 111, 110, 109},
+  {1, 1, 0, 3, 2, 9, 6, 6, 14, 3, 14, 9, 18, 18, 6, 9, 30, 21, 30, 22, 14, 6, 20, 13, 6, 49, 44, 39, 34, 29, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 115, 114, 113, 112, 111},
+  {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {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, 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, 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, -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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+  {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {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, 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, 1, 1, 1, 1, 1, 1},
+  {INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX},
+  {INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN},
+  {-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, -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, -1, -1, -1, -1, -1, -1},
+  {16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16},
+  {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},
+  {1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024},
+  {65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535},
+  {-1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023},
+  {INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX},
+  {0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, },
+  {0, 0, 2, 0, 0, 1, 6, 9, 4, 12, 6, 13, 12, 0, 2, 21, 28, 20, 12, 4, 16, 9, 2, 41, 36, 31, 26, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93},
+  {-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, -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, -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, -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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+  {65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535},
+  {INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX},
+  {16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16},
+  {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},
+  {0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, 0, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, },
+  {1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024},
+  {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, },
+  {1, 1, 0, 3, 2, 5, 6, 2, 6, 3, 0, 19, 18, 17, 16, 0, 13, 11, 9, 7, 5, 3, 1, -3000, -3000, -3000, -3000, -3000, -3000, -3000, 0, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000, -3000},
+  {0, 0, 2, 5, 4, 4, 2, 3, 4, 11, 4, 21, 20, 8, 10, 29, 20, 28, 20, 12, 4, 17, 10, 3, 44, 39, 34, 29, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 109, 108, 107, 106, 105, 104, 103, 102, 101},
+  {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, 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, 1, 1, 1, 1, 1, 1},
+  {1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0},
+  {-0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0, -0},
+  {1, 1, 2, 1, 6, 9, 10, 7, 2, 10, 4, 11, 10, 11, 0, 19, 26, 18, 10, 2, 14, 7, 0, 39, 34, 29, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91},
+  {0, 0, 2, 4, 0, 7, 4, 4, 12, 1, 12, 7, 16, 16, 4, 7, 28, 19, 28, 20, 12, 4, 18, 11, 4, 47, 42, 37, 32, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 114, 113, 112, 111, 110, 109},
+  {1, 1, 0, 2, 2, 3, 8, 11, 6, 14, 8, 15, 14, 2, 4, 23, 30, 22, 14, 6, 18, 11, 4, 43, 38, 33, 28, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95},
+  {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, 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, 1, 1, 1, 1, 1, 1},
+  {INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN, INT_MIN},
+  {0, 0, 0, 4, 0, 0, 10, 13, 0, 16, 0, 17, 16, 4, 6, 25, 16, 24, 16, 8, 0, 13, 6, 45, 40, 35, 30, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97},
+  {1, 1, 2, 3, 2, 2, 0, 1, 2, 9, 2, 19, 18, 6, 8, 27, 18, 26, 18, 10, 2, 15, 8, 1, 42, 37, 32, 27, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 107, 106, 105, 104, 103, 102, 101, 100, 99},
+  {1, 1, 0, 1, 6, 6, 4, 5, 6, 13, 6, 1, 22, 10, 12, 1, 22, 30, 22, 14, 6, 19, 12, 5, 46, 41, 36, 31, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 110, 109, 108, 107, 106, 105, 104, 103},
+  {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {-1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023, -1023},
+  {0, 0, 0, 0, 4, 8, 0, 0, 8, 15, 8, 3, 12, 12, 0, 3, 24, 32, 24, 16, 8, 0, 14, 7, 0, 43, 38, 33, 28, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 111, 110, 109, 108, 107, 106, 105},
+  {1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824},
+  {1, 1, 2, 2, 6, 5, 2, 2, 10, 17, 10, 5, 14, 14, 2, 5, 26, 17, 26, 18, 10, 2, 16, 9, 2, 45, 40, 35, 30, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2, 113, 112, 111, 110, 109, 108, 107},
+  {1, 1, 0, 3, 2, 9, 6, 6, 14, 3, 14, 9, 18, 18, 6, 9, 30, 21, 30, 22, 14, 6, 20, 13, 6, 49, 44, 39, 34, 29, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 115, 114, 113, 112, 111},
+  {INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MIN, INT_MAX, INT_MAX, INT_MAX} };