#define _LP64 1
#define __APPLE_CC__ 6000
#define __APPLE__ 1
#define __ATOMIC_ACQUIRE 2
#define __ATOMIC_ACQ_REL 4
#define __ATOMIC_CONSUME 1
#define __ATOMIC_RELAXED 0
#define __ATOMIC_RELEASE 3
#define __ATOMIC_SEQ_CST 5
#define __BIGGEST_ALIGNMENT__ 16
#define __BLOCKS__ 1
#define __BYTE_ORDER__ __ORDER_LITTLE_ENDIAN__
#define __CHAR16_TYPE__ unsigned short
#define __CHAR32_TYPE__ unsigned int
#define __CHAR_BIT__ 8
#define __CLANG_ATOMIC_BOOL_LOCK_FREE 2
#define __CLANG_ATOMIC_CHAR16_T_LOCK_FREE 2
#define __CLANG_ATOMIC_CHAR32_T_LOCK_FREE 2
#define __CLANG_ATOMIC_CHAR8_T_LOCK_FREE 2
#define __CLANG_ATOMIC_CHAR_LOCK_FREE 2
#define __CLANG_ATOMIC_INT_LOCK_FREE 2
#define __CLANG_ATOMIC_LLONG_LOCK_FREE 2
#define __CLANG_ATOMIC_LONG_LOCK_FREE 2
#define __CLANG_ATOMIC_POINTER_LOCK_FREE 2
#define __CLANG_ATOMIC_SHORT_LOCK_FREE 2
#define __CLANG_ATOMIC_WCHAR_T_LOCK_FREE 2
#define __CONSTANT_CFSTRINGS__ 1
#define __DBL_DECIMAL_DIG__ 17
#define __DBL_DENORM_MIN__ 4.9406564584124654e-324
#define __DBL_DIG__ 15
#define __DBL_EPSILON__ 2.2204460492503131e-16
#define __DBL_HAS_DENORM__ 1
#define __DBL_HAS_INFINITY__ 1
#define __DBL_HAS_QUIET_NAN__ 1
#define __DBL_MANT_DIG__ 53
#define __DBL_MAX_10_EXP__ 308
#define __DBL_MAX_EXP__ 1024
#define __DBL_MAX__ 1.7976931348623157e+308
#define __DBL_MIN_10_EXP__ (-307)
#define __DBL_MIN_EXP__ (-1021)
#define __DBL_MIN__ 2.2250738585072014e-308
#define __DECIMAL_DIG__ __LDBL_DECIMAL_DIG__
#define __DEPRECATED 1
#define __DYNAMIC__ 1
#define __ENVIRONMENT_MAC_OS_X_VERSION_MIN_REQUIRED__ 120000
#define __ENVIRONMENT_OS_VERSION_MIN_REQUIRED__ 120000
#define __EXCEPTIONS 1
#define __FINITE_MATH_ONLY__ 0
#define __FLT16_DECIMAL_DIG__ 5
#define __FLT16_DENORM_MIN__ 5.9604644775390625e-8F16
#define __FLT16_DIG__ 3
#define __FLT16_EPSILON__ 9.765625e-4F16
#define __FLT16_HAS_DENORM__ 1
#define __FLT16_HAS_INFINITY__ 1
#define __FLT16_HAS_QUIET_NAN__ 1
#define __FLT16_MANT_DIG__ 11
#define __FLT16_MAX_10_EXP__ 4
#define __FLT16_MAX_EXP__ 16
#define __FLT16_MAX__ 6.5504e+4F16
#define __FLT16_MIN_10_EXP__ (-4)
#define __FLT16_MIN_EXP__ (-13)
#define __FLT16_MIN__ 6.103515625e-5F16
#define __FLT_DECIMAL_DIG__ 9
#define __FLT_DENORM_MIN__ 1.40129846e-45F
#define __FLT_DIG__ 6
#define __FLT_EPSILON__ 1.19209290e-7F
#define __FLT_EVAL_METHOD__ 0
#define __FLT_HAS_DENORM__ 1
#define __FLT_HAS_INFINITY__ 1
#define __FLT_HAS_QUIET_NAN__ 1
#define __FLT_MANT_DIG__ 24
#define __FLT_MAX_10_EXP__ 38
#define __FLT_MAX_EXP__ 128
#define __FLT_MAX__ 3.40282347e+38F
#define __FLT_MIN_10_EXP__ (-37)
#define __FLT_MIN_EXP__ (-125)
#define __FLT_MIN__ 1.17549435e-38F
#define __FLT_RADIX__ 2
#define __FXSR__ 1
#define __GCC_ASM_FLAG_OUTPUTS__ 1
#define __GCC_ATOMIC_BOOL_LOCK_FREE 2
#define __GCC_ATOMIC_CHAR16_T_LOCK_FREE 2
#define __GCC_ATOMIC_CHAR32_T_LOCK_FREE 2
#define __GCC_ATOMIC_CHAR8_T_LOCK_FREE 2
#define __GCC_ATOMIC_CHAR_LOCK_FREE 2
#define __GCC_ATOMIC_INT_LOCK_FREE 2
#define __GCC_ATOMIC_LLONG_LOCK_FREE 2
#define __GCC_ATOMIC_LONG_LOCK_FREE 2
#define __GCC_ATOMIC_POINTER_LOCK_FREE 2
#define __GCC_ATOMIC_SHORT_LOCK_FREE 2
#define __GCC_ATOMIC_TEST_AND_SET_TRUEVAL 1
#define __GCC_ATOMIC_WCHAR_T_LOCK_FREE 2
#define __GCC_HAVE_SYNC_COMPARE_AND_SWAP_1 1
#define __GCC_HAVE_SYNC_COMPARE_AND_SWAP_16 1
#define __GCC_HAVE_SYNC_COMPARE_AND_SWAP_2 1
#define __GCC_HAVE_SYNC_COMPARE_AND_SWAP_4 1
#define __GCC_HAVE_SYNC_COMPARE_AND_SWAP_8 1
#define __GNUC_GNU_INLINE__ 1
#define __GNUC_MINOR__ 2
#define __GNUC_PATCHLEVEL__ 1
#define __GNUC__ 4
#define __GNUG__ 4
#define __GXX_ABI_VERSION 1002
#define __GXX_EXPERIMENTAL_CXX0X__ 1
#define __GXX_RTTI 1
#define __GXX_WEAK__ 1
#define __INT16_C_SUFFIX__ 
#define __INT16_FMTd__ "hd"
#define __INT16_FMTi__ "hi"
#define __INT16_MAX__ 32767
#define __INT16_TYPE__ short
#define __INT32_C_SUFFIX__ 
#define __INT32_FMTd__ "d"
#define __INT32_FMTi__ "i"
#define __INT32_MAX__ 2147483647
#define __INT32_TYPE__ int
#define __INT64_C_SUFFIX__ LL
#define __INT64_FMTd__ "lld"
#define __INT64_FMTi__ "lli"
#define __INT64_MAX__ 9223372036854775807LL
#define __INT64_TYPE__ long long int
#define __INT8_C_SUFFIX__ 
#define __INT8_FMTd__ "hhd"
#define __INT8_FMTi__ "hhi"
#define __INT8_MAX__ 127
#define __INT8_TYPE__ signed char
#define __INTMAX_C_SUFFIX__ L
#define __INTMAX_FMTd__ "ld"
#define __INTMAX_FMTi__ "li"
#define __INTMAX_MAX__ 9223372036854775807L
#define __INTMAX_TYPE__ long int
#define __INTMAX_WIDTH__ 64
#define __INTPTR_FMTd__ "ld"
#define __INTPTR_FMTi__ "li"
#define __INTPTR_MAX__ 9223372036854775807L
#define __INTPTR_TYPE__ long int
#define __INTPTR_WIDTH__ 64
#define __INT_FAST16_FMTd__ "hd"
#define __INT_FAST16_FMTi__ "hi"
#define __INT_FAST16_MAX__ 32767
#define __INT_FAST16_TYPE__ short
#define __INT_FAST32_FMTd__ "d"
#define __INT_FAST32_FMTi__ "i"
#define __INT_FAST32_MAX__ 2147483647
#define __INT_FAST32_TYPE__ int
#define __INT_FAST64_FMTd__ "lld"
#define __INT_FAST64_FMTi__ "lli"
#define __INT_FAST64_MAX__ 9223372036854775807LL
#define __INT_FAST64_TYPE__ long long int
#define __INT_FAST8_FMTd__ "hhd"
#define __INT_FAST8_FMTi__ "hhi"
#define __INT_FAST8_MAX__ 127
#define __INT_FAST8_TYPE__ signed char
#define __INT_LEAST16_FMTd__ "hd"
#define __INT_LEAST16_FMTi__ "hi"
#define __INT_LEAST16_MAX__ 32767
#define __INT_LEAST16_TYPE__ short
#define __INT_LEAST32_FMTd__ "d"
#define __INT_LEAST32_FMTi__ "i"
#define __INT_LEAST32_MAX__ 2147483647
#define __INT_LEAST32_TYPE__ int
#define __INT_LEAST64_FMTd__ "lld"
#define __INT_LEAST64_FMTi__ "lli"
#define __INT_LEAST64_MAX__ 9223372036854775807LL
#define __INT_LEAST64_TYPE__ long long int
#define __INT_LEAST8_FMTd__ "hhd"
#define __INT_LEAST8_FMTi__ "hhi"
#define __INT_LEAST8_MAX__ 127
#define __INT_LEAST8_TYPE__ signed char
#define __INT_MAX__ 2147483647
#define __LAHF_SAHF__ 1
#define __LDBL_DECIMAL_DIG__ 21
#define __LDBL_DENORM_MIN__ 3.64519953188247460253e-4951L
#define __LDBL_DIG__ 18
#define __LDBL_EPSILON__ 1.08420217248550443401e-19L
#define __LDBL_HAS_DENORM__ 1
#define __LDBL_HAS_INFINITY__ 1
#define __LDBL_HAS_QUIET_NAN__ 1
#define __LDBL_MANT_DIG__ 64
#define __LDBL_MAX_10_EXP__ 4932
#define __LDBL_MAX_EXP__ 16384
#define __LDBL_MAX__ 1.18973149535723176502e+4932L
#define __LDBL_MIN_10_EXP__ (-4931)
#define __LDBL_MIN_EXP__ (-16381)
#define __LDBL_MIN__ 3.36210314311209350626e-4932L
#define __LITTLE_ENDIAN__ 1
#define __LONG_LONG_MAX__ 9223372036854775807LL
#define __LONG_MAX__ 9223372036854775807L
#define __LP64__ 1
#define __MACH__ 1
#define __MMX__ 1
#define __NO_INLINE__ 1
#define __NO_MATH_INLINES 1
#define __OBJC_BOOL_IS_BOOL 0
#define __OPENCL_MEMORY_SCOPE_ALL_SVM_DEVICES 3
#define __OPENCL_MEMORY_SCOPE_DEVICE 2
#define __OPENCL_MEMORY_SCOPE_SUB_GROUP 4
#define __OPENCL_MEMORY_SCOPE_WORK_GROUP 1
#define __OPENCL_MEMORY_SCOPE_WORK_ITEM 0
#define __ORDER_BIG_ENDIAN__ 4321
#define __ORDER_LITTLE_ENDIAN__ 1234
#define __ORDER_PDP_ENDIAN__ 3412
#define __PIC__ 2
#define __POINTER_WIDTH__ 64
#define __PRAGMA_REDEFINE_EXTNAME 1
#define __PTRDIFF_FMTd__ "ld"
#define __PTRDIFF_FMTi__ "li"
#define __PTRDIFF_MAX__ 9223372036854775807L
#define __PTRDIFF_TYPE__ long int
#define __PTRDIFF_WIDTH__ 64
#define __REGISTER_PREFIX__ 
#define __SCHAR_MAX__ 127
#define __SEG_FS 1
#define __SEG_GS 1
#define __SHRT_MAX__ 32767
#define __SIG_ATOMIC_MAX__ 2147483647
#define __SIG_ATOMIC_WIDTH__ 32
#define __SIZEOF_DOUBLE__ 8
#define __SIZEOF_FLOAT__ 4
#define __SIZEOF_INT128__ 16
#define __SIZEOF_INT__ 4
#define __SIZEOF_LONG_DOUBLE__ 16
#define __SIZEOF_LONG_LONG__ 8
#define __SIZEOF_LONG__ 8
#define __SIZEOF_POINTER__ 8
#define __SIZEOF_PTRDIFF_T__ 8
#define __SIZEOF_SHORT__ 2
#define __SIZEOF_SIZE_T__ 8
#define __SIZEOF_WCHAR_T__ 4
#define __SIZEOF_WINT_T__ 4
#define __SIZE_FMTX__ "lX"
#define __SIZE_FMTo__ "lo"
#define __SIZE_FMTu__ "lu"
#define __SIZE_FMTx__ "lx"
#define __SIZE_MAX__ 18446744073709551615UL
#define __SIZE_TYPE__ long unsigned int
#define __SIZE_WIDTH__ 64
#define __SSE2_MATH__ 1
#define __SSE2__ 1
#define __SSE3__ 1
#define __SSE4_1__ 1
#define __SSE_MATH__ 1
#define __SSE__ 1
#define __SSP__ 1
#define __SSSE3__ 1
#define __STDCPP_DEFAULT_NEW_ALIGNMENT__ 16UL
#define __STDCPP_THREADS__ 1
#define __STDC_HOSTED__ 1
#define __STDC_NO_THREADS__ 1
#define __STDC_UTF_16__ 1
#define __STDC_UTF_32__ 1
#define __STDC__ 1
#define __STRICT_ANSI__ 1
#define __UINT16_C_SUFFIX__ 
#define __UINT16_FMTX__ "hX"
#define __UINT16_FMTo__ "ho"
#define __UINT16_FMTu__ "hu"
#define __UINT16_FMTx__ "hx"
#define __UINT16_MAX__ 65535
#define __UINT16_TYPE__ unsigned short
#define __UINT32_C_SUFFIX__ U
#define __UINT32_FMTX__ "X"
#define __UINT32_FMTo__ "o"
#define __UINT32_FMTu__ "u"
#define __UINT32_FMTx__ "x"
#define __UINT32_MAX__ 4294967295U
#define __UINT32_TYPE__ unsigned int
#define __UINT64_C_SUFFIX__ ULL
#define __UINT64_FMTX__ "llX"
#define __UINT64_FMTo__ "llo"
#define __UINT64_FMTu__ "llu"
#define __UINT64_FMTx__ "llx"
#define __UINT64_MAX__ 18446744073709551615ULL
#define __UINT64_TYPE__ long long unsigned int
#define __UINT8_C_SUFFIX__ 
#define __UINT8_FMTX__ "hhX"
#define __UINT8_FMTo__ "hho"
#define __UINT8_FMTu__ "hhu"
#define __UINT8_FMTx__ "hhx"
#define __UINT8_MAX__ 255
#define __UINT8_TYPE__ unsigned char
#define __UINTMAX_C_SUFFIX__ UL
#define __UINTMAX_FMTX__ "lX"
#define __UINTMAX_FMTo__ "lo"
#define __UINTMAX_FMTu__ "lu"
#define __UINTMAX_FMTx__ "lx"
#define __UINTMAX_MAX__ 18446744073709551615UL
#define __UINTMAX_TYPE__ long unsigned int
#define __UINTMAX_WIDTH__ 64
#define __UINTPTR_FMTX__ "lX"
#define __UINTPTR_FMTo__ "lo"
#define __UINTPTR_FMTu__ "lu"
#define __UINTPTR_FMTx__ "lx"
#define __UINTPTR_MAX__ 18446744073709551615UL
#define __UINTPTR_TYPE__ long unsigned int
#define __UINTPTR_WIDTH__ 64
#define __UINT_FAST16_FMTX__ "hX"
#define __UINT_FAST16_FMTo__ "ho"
#define __UINT_FAST16_FMTu__ "hu"
#define __UINT_FAST16_FMTx__ "hx"
#define __UINT_FAST16_MAX__ 65535
#define __UINT_FAST16_TYPE__ unsigned short
#define __UINT_FAST32_FMTX__ "X"
#define __UINT_FAST32_FMTo__ "o"
#define __UINT_FAST32_FMTu__ "u"
#define __UINT_FAST32_FMTx__ "x"
#define __UINT_FAST32_MAX__ 4294967295U
#define __UINT_FAST32_TYPE__ unsigned int
#define __UINT_FAST64_FMTX__ "llX"
#define __UINT_FAST64_FMTo__ "llo"
#define __UINT_FAST64_FMTu__ "llu"
#define __UINT_FAST64_FMTx__ "llx"
#define __UINT_FAST64_MAX__ 18446744073709551615ULL
#define __UINT_FAST64_TYPE__ long long unsigned int
#define __UINT_FAST8_FMTX__ "hhX"
#define __UINT_FAST8_FMTo__ "hho"
#define __UINT_FAST8_FMTu__ "hhu"
#define __UINT_FAST8_FMTx__ "hhx"
#define __UINT_FAST8_MAX__ 255
#define __UINT_FAST8_TYPE__ unsigned char
#define __UINT_LEAST16_FMTX__ "hX"
#define __UINT_LEAST16_FMTo__ "ho"
#define __UINT_LEAST16_FMTu__ "hu"
#define __UINT_LEAST16_FMTx__ "hx"
#define __UINT_LEAST16_MAX__ 65535
#define __UINT_LEAST16_TYPE__ unsigned short
#define __UINT_LEAST32_FMTX__ "X"
#define __UINT_LEAST32_FMTo__ "o"
#define __UINT_LEAST32_FMTu__ "u"
#define __UINT_LEAST32_FMTx__ "x"
#define __UINT_LEAST32_MAX__ 4294967295U
#define __UINT_LEAST32_TYPE__ unsigned int
#define __UINT_LEAST64_FMTX__ "llX"
#define __UINT_LEAST64_FMTo__ "llo"
#define __UINT_LEAST64_FMTu__ "llu"
#define __UINT_LEAST64_FMTx__ "llx"
#define __UINT_LEAST64_MAX__ 18446744073709551615ULL
#define __UINT_LEAST64_TYPE__ long long unsigned int
#define __UINT_LEAST8_FMTX__ "hhX"
#define __UINT_LEAST8_FMTo__ "hho"
#define __UINT_LEAST8_FMTu__ "hhu"
#define __UINT_LEAST8_FMTx__ "hhx"
#define __UINT_LEAST8_MAX__ 255
#define __UINT_LEAST8_TYPE__ unsigned char
#define __USER_LABEL_PREFIX__ _
#define __VERSION__ "Apple LLVM 13.0.0 (clang-1300.0.29.30)"
#define __WCHAR_MAX__ 2147483647
#define __WCHAR_TYPE__ int
#define __WCHAR_WIDTH__ 32
#define __WINT_MAX__ 2147483647
#define __WINT_TYPE__ int
#define __WINT_WIDTH__ 32
#define __amd64 1
#define __amd64__ 1
#define __apple_build_version__ 13000029
#define __block __attribute__((__blocks__(byref)))
#define __clang__ 1
#define __clang_major__ 13
#define __clang_minor__ 0
#define __clang_patchlevel__ 0
#define __clang_version__ "13.0.0 (clang-1300.0.29.30)"
#define __code_model_small__ 1
#define __core2 1
#define __core2__ 1
#define __cplusplus 202002L
#define __cpp_aggregate_bases 201603L
#define __cpp_aggregate_nsdmi 201304L
#define __cpp_alias_templates 200704L
#define __cpp_aligned_new 201606L
#define __cpp_attributes 200809L
#define __cpp_binary_literals 201304L
#define __cpp_capture_star_this 201603L
#define __cpp_char8_t 201811L
#define __cpp_concepts 201907L
#define __cpp_conditional_explicit 201806L
#define __cpp_constexpr 201907L
#define __cpp_constexpr_dynamic_alloc 201907L
#define __cpp_constexpr_in_decltype 201711L
#define __cpp_constinit 201907L
#define __cpp_coroutines 201703L
#define __cpp_decltype 200707L
#define __cpp_decltype_auto 201304L
#define __cpp_deduction_guides 201703L
#define __cpp_delegating_constructors 200604L
#define __cpp_designated_initializers 201707L
#define __cpp_digit_separators 201309L
#define __cpp_enumerator_attributes 201411L
#define __cpp_exceptions 199711L
#define __cpp_fold_expressions 201603L
#define __cpp_generic_lambdas 201707L
#define __cpp_guaranteed_copy_elision 201606L
#define __cpp_hex_float 201603L
#define __cpp_if_constexpr 201606L
#define __cpp_impl_destroying_delete 201806L
#define __cpp_impl_three_way_comparison 201907L
#define __cpp_inheriting_constructors 201511L
#define __cpp_init_captures 201803L
#define __cpp_initializer_lists 200806L
#define __cpp_inline_variables 201606L
#define __cpp_lambdas 200907L
#define __cpp_namespace_attributes 201411L
#define __cpp_nested_namespace_definitions 201411L
#define __cpp_noexcept_function_type 201510L
#define __cpp_nontype_template_args 201911L
#define __cpp_nontype_template_parameter_auto 201606L
#define __cpp_nsdmi 200809L
#define __cpp_range_based_for 201603L
#define __cpp_raw_strings 200710L
#define __cpp_ref_qualifiers 200710L
#define __cpp_return_type_deduction 201304L
#define __cpp_rtti 199711L
#define __cpp_rvalue_references 200610L
#define __cpp_static_assert 201411L
#define __cpp_structured_bindings 201606L
#define __cpp_template_auto 201606L
#define __cpp_threadsafe_static_init 200806L
#define __cpp_unicode_characters 200704L
#define __cpp_unicode_literals 200710L
#define __cpp_user_defined_literals 200809L
#define __cpp_variable_templates 201304L
#define __cpp_variadic_templates 200704L
#define __cpp_variadic_using 201611L
#define __llvm__ 1
#define __nonnull _Nonnull
#define __null_unspecified _Null_unspecified
#define __nullable _Nullable
#define __pic__ 2
#define __private_extern__ extern
#define __seg_fs __attribute__((address_space(257)))
#define __seg_gs __attribute__((address_space(256)))
#define __strong 
#define __tune_core2__ 1
#define __unsafe_unretained 
#define __weak __attribute__((objc_gc(weak)))
#define __x86_64 1
#define __x86_64__ 1
