Restoring authorship annotation for Andrey Khalyavin <[email protected]>. Commit 1 of 2.

1 files changed, 523 insertions, 523 deletions

diff --git a/contrib/libs/cxxsupp/libcxx/include/ratio b/contrib/libs/cxxsupp/libcxx/include/ratio
index 16d3b2b831e..0903be03285 100644
--- a/contrib/libs/cxxsupp/libcxx/include/ratio
+++ b/contrib/libs/cxxsupp/libcxx/include/ratio
@@ -1,526 +1,526 @@
-// -*- C++ -*-
-//===---------------------------- ratio -----------------------------------===//
-//
+// -*- C++ -*- 
+//===---------------------------- ratio -----------------------------------===// 
+// 
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-#ifndef _LIBCPP_RATIO
-#define _LIBCPP_RATIO
-
-/*
-    ratio synopsis
-
-namespace std
-{
-
-template <intmax_t N, intmax_t D = 1>
-class ratio
-{
-public:
-    static constexpr intmax_t num;
-    static constexpr intmax_t den;
-    typedef ratio<num, den> type;
-};
-
-// ratio arithmetic
-template <class R1, class R2> using ratio_add = ...;
-template <class R1, class R2> using ratio_subtract = ...;
-template <class R1, class R2> using ratio_multiply = ...;
-template <class R1, class R2> using ratio_divide = ...;
-
-// ratio comparison
-template <class R1, class R2> struct ratio_equal;
-template <class R1, class R2> struct ratio_not_equal;
-template <class R1, class R2> struct ratio_less;
-template <class R1, class R2> struct ratio_less_equal;
-template <class R1, class R2> struct ratio_greater;
-template <class R1, class R2> struct ratio_greater_equal;
-
-// convenience SI typedefs
-typedef ratio<1, 1000000000000000000000000> yocto;  // not supported
-typedef ratio<1,    1000000000000000000000> zepto;  // not supported
-typedef ratio<1,       1000000000000000000> atto;
-typedef ratio<1,          1000000000000000> femto;
-typedef ratio<1,             1000000000000> pico;
-typedef ratio<1,                1000000000> nano;
-typedef ratio<1,                   1000000> micro;
-typedef ratio<1,                      1000> milli;
-typedef ratio<1,                       100> centi;
-typedef ratio<1,                        10> deci;
-typedef ratio<                       10, 1> deca;
-typedef ratio<                      100, 1> hecto;
-typedef ratio<                     1000, 1> kilo;
-typedef ratio<                  1000000, 1> mega;
-typedef ratio<               1000000000, 1> giga;
-typedef ratio<            1000000000000, 1> tera;
-typedef ratio<         1000000000000000, 1> peta;
-typedef ratio<      1000000000000000000, 1> exa;
-typedef ratio<   1000000000000000000000, 1> zetta;  // not supported
-typedef ratio<1000000000000000000000000, 1> yotta;  // not supported
-
-  // 20.11.5, ratio comparison
-  template <class R1, class R2> inline constexpr bool ratio_equal_v
-    = ratio_equal<R1, R2>::value;                                       // C++17
-  template <class R1, class R2> inline constexpr bool ratio_not_equal_v
-    = ratio_not_equal<R1, R2>::value;                                   // C++17
-  template <class R1, class R2> inline constexpr bool ratio_less_v
-    = ratio_less<R1, R2>::value;                                        // C++17
-  template <class R1, class R2> inline constexpr bool ratio_less_equal_v
-    = ratio_less_equal<R1, R2>::value;                                  // C++17
-  template <class R1, class R2> inline constexpr bool ratio_greater_v
-    = ratio_greater<R1, R2>::value;                                     // C++17
-  template <class R1, class R2> inline constexpr bool ratio_greater_equal_v
-    = ratio_greater_equal<R1, R2>::value;                               // C++17
-}
-*/
-
-#include <__config>
-#include <climits>
-#include <cstdint>
-#include <type_traits>
-
-#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
-#pragma GCC system_header
-#endif
-
-_LIBCPP_PUSH_MACROS
-#include <__undef_macros>
-
-
-_LIBCPP_BEGIN_NAMESPACE_STD
-
-// __static_gcd
-
-template <intmax_t _Xp, intmax_t _Yp>
-struct __static_gcd
-{
-    static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value;
-};
-
-template <intmax_t _Xp>
-struct __static_gcd<_Xp, 0>
-{
-    static const intmax_t value = _Xp;
-};
-
-template <>
-struct __static_gcd<0, 0>
-{
-    static const intmax_t value = 1;
-};
-
-// __static_lcm
-
-template <intmax_t _Xp, intmax_t _Yp>
-struct __static_lcm
-{
-    static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp;
-};
-
-template <intmax_t _Xp>
-struct __static_abs
-{
-    static const intmax_t value = _Xp < 0 ? -_Xp : _Xp;
-};
-
-template <intmax_t _Xp>
-struct __static_sign
-{
-    static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1);
-};
-
-template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
-class __ll_add;
-
-template <intmax_t _Xp, intmax_t _Yp>
-class __ll_add<_Xp, _Yp, 1>
-{
-    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
-    static const intmax_t max = -min;
-
-    static_assert(_Xp <= max - _Yp, "overflow in __ll_add");
-public:
-    static const intmax_t value = _Xp + _Yp;
-};
-
-template <intmax_t _Xp, intmax_t _Yp>
-class __ll_add<_Xp, _Yp, 0>
-{
-public:
-    static const intmax_t value = _Xp;
-};
-
-template <intmax_t _Xp, intmax_t _Yp>
-class __ll_add<_Xp, _Yp, -1>
-{
-    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
-    static const intmax_t max = -min;
-
-    static_assert(min - _Yp <= _Xp, "overflow in __ll_add");
-public:
-    static const intmax_t value = _Xp + _Yp;
-};
-
-template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
-class __ll_sub;
-
-template <intmax_t _Xp, intmax_t _Yp>
-class __ll_sub<_Xp, _Yp, 1>
-{
-    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
-    static const intmax_t max = -min;
-
-    static_assert(min + _Yp <= _Xp, "overflow in __ll_sub");
-public:
-    static const intmax_t value = _Xp - _Yp;
-};
-
-template <intmax_t _Xp, intmax_t _Yp>
-class __ll_sub<_Xp, _Yp, 0>
-{
-public:
-    static const intmax_t value = _Xp;
-};
-
-template <intmax_t _Xp, intmax_t _Yp>
-class __ll_sub<_Xp, _Yp, -1>
-{
-    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
-    static const intmax_t max = -min;
-
-    static_assert(_Xp <= max + _Yp, "overflow in __ll_sub");
-public:
-    static const intmax_t value = _Xp - _Yp;
-};
-
-template <intmax_t _Xp, intmax_t _Yp>
-class __ll_mul
-{
-    static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
-    static const intmax_t min = nan + 1;
-    static const intmax_t max = -min;
-    static const intmax_t __a_x = __static_abs<_Xp>::value;
-    static const intmax_t __a_y = __static_abs<_Yp>::value;
-
-    static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul");
-public:
-    static const intmax_t value = _Xp * _Yp;
-};
-
-template <intmax_t _Yp>
-class __ll_mul<0, _Yp>
-{
-public:
-    static const intmax_t value = 0;
-};
-
-template <intmax_t _Xp>
-class __ll_mul<_Xp, 0>
-{
-public:
-    static const intmax_t value = 0;
-};
-
-template <>
-class __ll_mul<0, 0>
-{
-public:
-    static const intmax_t value = 0;
-};
-
-// Not actually used but left here in case needed in future maintenance
-template <intmax_t _Xp, intmax_t _Yp>
-class __ll_div
-{
-    static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
-    static const intmax_t min = nan + 1;
-    static const intmax_t max = -min;
-
-    static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div");
-public:
-    static const intmax_t value = _Xp / _Yp;
-};
-
-template <intmax_t _Num, intmax_t _Den = 1>
-class _LIBCPP_TEMPLATE_VIS ratio
-{
-    static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range");
-    static_assert(_Den != 0, "ratio divide by 0");
-    static_assert(__static_abs<_Den>::value >  0, "ratio denominator is out of range");
-    static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value;
-    static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value;
-    static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value;
-    static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value;
-public:
-    static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd;
-    static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd;
-
-    typedef ratio<num, den> type;
-};
-
-template <intmax_t _Num, intmax_t _Den>
-_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num;
-
-template <intmax_t _Num, intmax_t _Den>
-_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den;
-
-template <class _Tp>                    struct __is_ratio                     : false_type {};
-template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type  {};
-
-typedef ratio<1LL, 1000000000000000000LL> atto;
-typedef ratio<1LL,    1000000000000000LL> femto;
-typedef ratio<1LL,       1000000000000LL> pico;
-typedef ratio<1LL,          1000000000LL> nano;
-typedef ratio<1LL,             1000000LL> micro;
-typedef ratio<1LL,                1000LL> milli;
-typedef ratio<1LL,                 100LL> centi;
-typedef ratio<1LL,                  10LL> deci;
-typedef ratio<                 10LL, 1LL> deca;
-typedef ratio<                100LL, 1LL> hecto;
-typedef ratio<               1000LL, 1LL> kilo;
-typedef ratio<            1000000LL, 1LL> mega;
-typedef ratio<         1000000000LL, 1LL> giga;
-typedef ratio<      1000000000000LL, 1LL> tera;
-typedef ratio<   1000000000000000LL, 1LL> peta;
-typedef ratio<1000000000000000000LL, 1LL> exa;
-
-template <class _R1, class _R2>
-struct __ratio_multiply
-{
-private:
-    static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value;
-    static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value;
-public:
-    typedef typename ratio
-        <
-            __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value,
-            __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value
-        >::type type;
-};
-
-#ifndef _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2> using ratio_multiply
-                                    = typename __ratio_multiply<_R1, _R2>::type;
-
-#else  // _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_multiply
-    : public __ratio_multiply<_R1, _R2>::type {};
-
-#endif // _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2>
-struct __ratio_divide
-{
-private:
-    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
-    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
-public:
-    typedef typename ratio
-        <
-            __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
-            __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
-        >::type type;
-};
-
-#ifndef _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2> using ratio_divide
-                                      = typename __ratio_divide<_R1, _R2>::type;
-
-#else  // _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_divide
-    : public __ratio_divide<_R1, _R2>::type {};
-
-#endif // _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2>
-struct __ratio_add
-{
-private:
-    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
-    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
-public:
-    typedef typename ratio_multiply
-        <
-            ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,
-            ratio
-            <
-                __ll_add
-                <
-                    __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
-                    __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
-                >::value,
-                _R2::den
-            >
-        >::type type;
-};
-
-#ifndef _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2> using ratio_add
-                                         = typename __ratio_add<_R1, _R2>::type;
-
-#else  // _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_add
-    : public __ratio_add<_R1, _R2>::type {};
-
-#endif // _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2>
-struct __ratio_subtract
-{
-private:
-    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
-    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
-public:
-    typedef typename ratio_multiply
-        <
-            ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,
-            ratio
-            <
-                __ll_sub
-                <
-                    __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
-                    __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
-                >::value,
-                _R2::den
-            >
-        >::type type;
-};
-
-#ifndef _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2> using ratio_subtract
-                                    = typename __ratio_subtract<_R1, _R2>::type;
-
-#else  // _LIBCPP_CXX03_LANG
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_subtract
-    : public __ratio_subtract<_R1, _R2>::type {};
-
-#endif // _LIBCPP_CXX03_LANG
-
-// ratio_equal
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_equal
-    : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {};
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_not_equal
-    : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {};
-
-// ratio_less
-
-template <class _R1, class _R2, bool _Odd = false,
-          intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den,
-          intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den>
-struct __ratio_less1
-{
-    static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2;
-};
-
-template <class _R1, class _R2, bool _Odd, intmax_t _Qp>
-struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0>
-{
-    static const bool value = false;
-};
-
-template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2>
-struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2>
-{
-    static const bool value = !_Odd;
-};
-
-template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1>
-struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0>
-{
-    static const bool value = _Odd;
-};
-
-template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1,
-                                                        intmax_t _M2>
-struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2>
-{
-    static const bool value = __ratio_less1<ratio<_R1::den, _M1>,
-                                            ratio<_R2::den, _M2>, !_Odd>::value;
-};
-
-template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value,
-                                intmax_t _S2 = __static_sign<_R2::num>::value>
-struct __ratio_less
-{
-    static const bool value = _S1 < _S2;
-};
-
-template <class _R1, class _R2>
-struct __ratio_less<_R1, _R2, 1LL, 1LL>
-{
-    static const bool value = __ratio_less1<_R1, _R2>::value;
-};
-
-template <class _R1, class _R2>
-struct __ratio_less<_R1, _R2, -1LL, -1LL>
-{
-    static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value;
-};
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_less
-    : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {};
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_less_equal
-    : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {};
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_greater
-    : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {};
-
-template <class _R1, class _R2>
-struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal
-    : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {};
-
-template <class _R1, class _R2>
-struct __ratio_gcd
-{
-    typedef ratio<__static_gcd<_R1::num, _R2::num>::value,
-                  __static_lcm<_R1::den, _R2::den>::value> type;
-};
-
-#if _LIBCPP_STD_VER > 14
-template <class _R1, class _R2>
-inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value;
-
-template <class _R1, class _R2>
-inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value;
-
-template <class _R1, class _R2>
-inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value;
-
-template <class _R1, class _R2>
-inline constexpr bool ratio_less_equal_v = ratio_less_equal<_R1, _R2>::value;
-
-template <class _R1, class _R2>
-inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value;
-
-template <class _R1, class _R2>
-inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value;
-#endif
-
-_LIBCPP_END_NAMESPACE_STD
-
-_LIBCPP_POP_MACROS
-
-#endif // _LIBCPP_RATIO
+// 
+//===----------------------------------------------------------------------===// 
+ 
+#ifndef _LIBCPP_RATIO 
+#define _LIBCPP_RATIO 
+ 
+/* 
+    ratio synopsis 
+ 
+namespace std 
+{ 
+ 
+template <intmax_t N, intmax_t D = 1> 
+class ratio 
+{ 
+public: 
+    static constexpr intmax_t num; 
+    static constexpr intmax_t den; 
+    typedef ratio<num, den> type; 
+}; 
+ 
+// ratio arithmetic 
+template <class R1, class R2> using ratio_add = ...; 
+template <class R1, class R2> using ratio_subtract = ...; 
+template <class R1, class R2> using ratio_multiply = ...; 
+template <class R1, class R2> using ratio_divide = ...; 
+ 
+// ratio comparison 
+template <class R1, class R2> struct ratio_equal; 
+template <class R1, class R2> struct ratio_not_equal; 
+template <class R1, class R2> struct ratio_less; 
+template <class R1, class R2> struct ratio_less_equal; 
+template <class R1, class R2> struct ratio_greater; 
+template <class R1, class R2> struct ratio_greater_equal; 
+ 
+// convenience SI typedefs 
+typedef ratio<1, 1000000000000000000000000> yocto;  // not supported 
+typedef ratio<1,    1000000000000000000000> zepto;  // not supported 
+typedef ratio<1,       1000000000000000000> atto; 
+typedef ratio<1,          1000000000000000> femto; 
+typedef ratio<1,             1000000000000> pico; 
+typedef ratio<1,                1000000000> nano; 
+typedef ratio<1,                   1000000> micro; 
+typedef ratio<1,                      1000> milli; 
+typedef ratio<1,                       100> centi; 
+typedef ratio<1,                        10> deci; 
+typedef ratio<                       10, 1> deca; 
+typedef ratio<                      100, 1> hecto; 
+typedef ratio<                     1000, 1> kilo; 
+typedef ratio<                  1000000, 1> mega; 
+typedef ratio<               1000000000, 1> giga; 
+typedef ratio<            1000000000000, 1> tera; 
+typedef ratio<         1000000000000000, 1> peta; 
+typedef ratio<      1000000000000000000, 1> exa; 
+typedef ratio<   1000000000000000000000, 1> zetta;  // not supported 
+typedef ratio<1000000000000000000000000, 1> yotta;  // not supported 
+ 
+  // 20.11.5, ratio comparison 
+  template <class R1, class R2> inline constexpr bool ratio_equal_v 
+    = ratio_equal<R1, R2>::value;                                       // C++17 
+  template <class R1, class R2> inline constexpr bool ratio_not_equal_v 
+    = ratio_not_equal<R1, R2>::value;                                   // C++17 
+  template <class R1, class R2> inline constexpr bool ratio_less_v 
+    = ratio_less<R1, R2>::value;                                        // C++17 
+  template <class R1, class R2> inline constexpr bool ratio_less_equal_v 
+    = ratio_less_equal<R1, R2>::value;                                  // C++17 
+  template <class R1, class R2> inline constexpr bool ratio_greater_v 
+    = ratio_greater<R1, R2>::value;                                     // C++17 
+  template <class R1, class R2> inline constexpr bool ratio_greater_equal_v 
+    = ratio_greater_equal<R1, R2>::value;                               // C++17 
+} 
+*/ 
+ 
+#include <__config> 
+#include <climits> 
+#include <cstdint> 
+#include <type_traits> 
+ 
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 
+#pragma GCC system_header 
+#endif 
+ 
+_LIBCPP_PUSH_MACROS 
+#include <__undef_macros> 
+ 
+ 
+_LIBCPP_BEGIN_NAMESPACE_STD 
+ 
+// __static_gcd 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+struct __static_gcd 
+{ 
+    static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 
+}; 
+ 
+template <intmax_t _Xp> 
+struct __static_gcd<_Xp, 0> 
+{ 
+    static const intmax_t value = _Xp; 
+}; 
+ 
+template <> 
+struct __static_gcd<0, 0> 
+{ 
+    static const intmax_t value = 1; 
+}; 
+ 
+// __static_lcm 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+struct __static_lcm 
+{ 
+    static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 
+}; 
+ 
+template <intmax_t _Xp> 
+struct __static_abs 
+{ 
+    static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 
+}; 
+ 
+template <intmax_t _Xp> 
+struct __static_sign 
+{ 
+    static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); 
+}; 
+ 
+template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 
+class __ll_add; 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+class __ll_add<_Xp, _Yp, 1> 
+{ 
+    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 
+    static const intmax_t max = -min; 
+ 
+    static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 
+public: 
+    static const intmax_t value = _Xp + _Yp; 
+}; 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+class __ll_add<_Xp, _Yp, 0> 
+{ 
+public: 
+    static const intmax_t value = _Xp; 
+}; 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+class __ll_add<_Xp, _Yp, -1> 
+{ 
+    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 
+    static const intmax_t max = -min; 
+ 
+    static_assert(min - _Yp <= _Xp, "overflow in __ll_add"); 
+public: 
+    static const intmax_t value = _Xp + _Yp; 
+}; 
+ 
+template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 
+class __ll_sub; 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+class __ll_sub<_Xp, _Yp, 1> 
+{ 
+    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 
+    static const intmax_t max = -min; 
+ 
+    static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 
+public: 
+    static const intmax_t value = _Xp - _Yp; 
+}; 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+class __ll_sub<_Xp, _Yp, 0> 
+{ 
+public: 
+    static const intmax_t value = _Xp; 
+}; 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+class __ll_sub<_Xp, _Yp, -1> 
+{ 
+    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 
+    static const intmax_t max = -min; 
+ 
+    static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 
+public: 
+    static const intmax_t value = _Xp - _Yp; 
+}; 
+ 
+template <intmax_t _Xp, intmax_t _Yp> 
+class __ll_mul 
+{ 
+    static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 
+    static const intmax_t min = nan + 1; 
+    static const intmax_t max = -min; 
+    static const intmax_t __a_x = __static_abs<_Xp>::value; 
+    static const intmax_t __a_y = __static_abs<_Yp>::value; 
+ 
+    static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 
+public: 
+    static const intmax_t value = _Xp * _Yp; 
+}; 
+ 
+template <intmax_t _Yp> 
+class __ll_mul<0, _Yp> 
+{ 
+public: 
+    static const intmax_t value = 0; 
+}; 
+ 
+template <intmax_t _Xp> 
+class __ll_mul<_Xp, 0> 
+{ 
+public: 
+    static const intmax_t value = 0; 
+}; 
+ 
+template <> 
+class __ll_mul<0, 0> 
+{ 
+public: 
+    static const intmax_t value = 0; 
+}; 
+ 
+// Not actually used but left here in case needed in future maintenance 
+template <intmax_t _Xp, intmax_t _Yp> 
+class __ll_div 
+{ 
+    static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 
+    static const intmax_t min = nan + 1; 
+    static const intmax_t max = -min; 
+ 
+    static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 
+public: 
+    static const intmax_t value = _Xp / _Yp; 
+}; 
+ 
+template <intmax_t _Num, intmax_t _Den = 1> 
+class _LIBCPP_TEMPLATE_VIS ratio 
+{ 
+    static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 
+    static_assert(_Den != 0, "ratio divide by 0"); 
+    static_assert(__static_abs<_Den>::value >  0, "ratio denominator is out of range"); 
+    static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 
+    static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 
+    static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 
+    static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 
+public: 
+    static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 
+    static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 
+ 
+    typedef ratio<num, den> type; 
+}; 
+ 
+template <intmax_t _Num, intmax_t _Den> 
+_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 
+ 
+template <intmax_t _Num, intmax_t _Den> 
+_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 
+ 
+template <class _Tp>                    struct __is_ratio                     : false_type {}; 
+template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type  {}; 
+ 
+typedef ratio<1LL, 1000000000000000000LL> atto; 
+typedef ratio<1LL,    1000000000000000LL> femto; 
+typedef ratio<1LL,       1000000000000LL> pico; 
+typedef ratio<1LL,          1000000000LL> nano; 
+typedef ratio<1LL,             1000000LL> micro; 
+typedef ratio<1LL,                1000LL> milli; 
+typedef ratio<1LL,                 100LL> centi; 
+typedef ratio<1LL,                  10LL> deci; 
+typedef ratio<                 10LL, 1LL> deca; 
+typedef ratio<                100LL, 1LL> hecto; 
+typedef ratio<               1000LL, 1LL> kilo; 
+typedef ratio<            1000000LL, 1LL> mega; 
+typedef ratio<         1000000000LL, 1LL> giga; 
+typedef ratio<      1000000000000LL, 1LL> tera; 
+typedef ratio<   1000000000000000LL, 1LL> peta; 
+typedef ratio<1000000000000000000LL, 1LL> exa; 
+ 
+template <class _R1, class _R2> 
+struct __ratio_multiply 
+{ 
+private: 
+    static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 
+    static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 
+public: 
+    typedef typename ratio 
+        < 
+            __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 
+            __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 
+        >::type type; 
+}; 
+ 
+#ifndef _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> using ratio_multiply 
+                                    = typename __ratio_multiply<_R1, _R2>::type; 
+ 
+#else  // _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_multiply 
+    : public __ratio_multiply<_R1, _R2>::type {}; 
+ 
+#endif // _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> 
+struct __ratio_divide 
+{ 
+private: 
+    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 
+    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 
+public: 
+    typedef typename ratio 
+        < 
+            __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 
+            __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 
+        >::type type; 
+}; 
+ 
+#ifndef _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> using ratio_divide 
+                                      = typename __ratio_divide<_R1, _R2>::type; 
+ 
+#else  // _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_divide 
+    : public __ratio_divide<_R1, _R2>::type {}; 
+ 
+#endif // _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> 
+struct __ratio_add 
+{ 
+private: 
+    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 
+    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 
+public: 
+    typedef typename ratio_multiply 
+        < 
+            ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 
+            ratio 
+            < 
+                __ll_add 
+                < 
+                    __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 
+                    __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 
+                >::value, 
+                _R2::den 
+            > 
+        >::type type; 
+}; 
+ 
+#ifndef _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> using ratio_add 
+                                         = typename __ratio_add<_R1, _R2>::type; 
+ 
+#else  // _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_add 
+    : public __ratio_add<_R1, _R2>::type {}; 
+ 
+#endif // _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> 
+struct __ratio_subtract 
+{ 
+private: 
+    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 
+    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 
+public: 
+    typedef typename ratio_multiply 
+        < 
+            ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 
+            ratio 
+            < 
+                __ll_sub 
+                < 
+                    __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 
+                    __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 
+                >::value, 
+                _R2::den 
+            > 
+        >::type type; 
+}; 
+ 
+#ifndef _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> using ratio_subtract 
+                                    = typename __ratio_subtract<_R1, _R2>::type; 
+ 
+#else  // _LIBCPP_CXX03_LANG 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_subtract 
+    : public __ratio_subtract<_R1, _R2>::type {}; 
+ 
+#endif // _LIBCPP_CXX03_LANG 
+ 
+// ratio_equal 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_equal 
+    : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {}; 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_not_equal 
+    : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {}; 
+ 
+// ratio_less 
+ 
+template <class _R1, class _R2, bool _Odd = false, 
+          intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 
+          intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 
+struct __ratio_less1 
+{ 
+    static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 
+}; 
+ 
+template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 
+struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 
+{ 
+    static const bool value = false; 
+}; 
+ 
+template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 
+struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 
+{ 
+    static const bool value = !_Odd; 
+}; 
+ 
+template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 
+struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 
+{ 
+    static const bool value = _Odd; 
+}; 
+ 
+template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 
+                                                        intmax_t _M2> 
+struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 
+{ 
+    static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 
+                                            ratio<_R2::den, _M2>, !_Odd>::value; 
+}; 
+ 
+template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 
+                                intmax_t _S2 = __static_sign<_R2::num>::value> 
+struct __ratio_less 
+{ 
+    static const bool value = _S1 < _S2; 
+}; 
+ 
+template <class _R1, class _R2> 
+struct __ratio_less<_R1, _R2, 1LL, 1LL> 
+{ 
+    static const bool value = __ratio_less1<_R1, _R2>::value; 
+}; 
+ 
+template <class _R1, class _R2> 
+struct __ratio_less<_R1, _R2, -1LL, -1LL> 
+{ 
+    static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 
+}; 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_less 
+    : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {}; 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_less_equal 
+    : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {}; 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_greater 
+    : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {}; 
+ 
+template <class _R1, class _R2> 
+struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal 
+    : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {}; 
+ 
+template <class _R1, class _R2> 
+struct __ratio_gcd 
+{ 
+    typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 
+                  __static_lcm<_R1::den, _R2::den>::value> type; 
+}; 
+ 
+#if _LIBCPP_STD_VER > 14 
+template <class _R1, class _R2> 
+inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 
+ 
+template <class _R1, class _R2> 
+inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 
+ 
+template <class _R1, class _R2> 
+inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 
+ 
+template <class _R1, class _R2> 
+inline constexpr bool ratio_less_equal_v = ratio_less_equal<_R1, _R2>::value; 
+ 
+template <class _R1, class _R2> 
+inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 
+ 
+template <class _R1, class _R2> 
+inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value; 
+#endif 
+ 
+_LIBCPP_END_NAMESPACE_STD 
+ 
+_LIBCPP_POP_MACROS 
+ 
+#endif // _LIBCPP_RATIO