Language: C++

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include<string>
#include<set>
#include<vector>
#include <sstream>
#include <cmath>
#include <cstdio>
#include <quadmath.h>

using namespace std;

typedef long double ld;

__float128 circumscribed_sphere(__float128 a,__float128 b,__float128 c,__float128 d,__float128 e,__float128 f){
 
  __float128 a2=a*a,b2=b*b,c2=c*c,d2=d*d,e2=e*e,f2=f*f;
  
  __float128 V=sqrt((a2*d2*((b2+e2+c2+f2)-(a2+d2))
	     +b2*e2*((c2+f2+a2+d2)-(b2+e2))
	     +c2*f2*((a2+d2+b2+e2)-(c2+f2)))
	    -(a2*e2*f2+d2*e2*f2+c2*d2*e2+a2*b2*c2))/12.0000000000L;
  
  return V;
}

int main(void){

  int N;
  while(cin >> N,N){
    vector<__float128>a(N);
    for(int i=0;i<N;i++)cin >> a[i];
    
    __float128 ans=0;
    for(int i=0;i<N;i++){
      for(int j=i+1;j<N;j++){
	for(int k=j+1;k<N;k++){
	  for(int l=k+1;l<N;l++){
	    for(int m=l+1;m<N;m++){
	      for(int n=m+1;n<N;n++){
		__float128 res=circumscribed_sphere(a[i],a[j],a[k],a[l],a[m],a[n]);
		ans=max(ans,res);
	      }
	    }
	  }
	}
      }
    }
    printf("%.6Qf\n",ans);

  }

  return 0;
}

Compiler output:
a.cc: In function '__float128 circumscribed_sphere(__float128, __float128, __float128, __float128, __float128, __float128)':
a.cc:21:20: error: call of overloaded 'sqrt(__float128)' is ambiguous
   21 |   __float128 V=sqrt((a2*d2*((b2+e2+c2+f2)-(a2+d2))
      |                ~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   22 |              +b2*e2*((c2+f2+a2+d2)-(b2+e2))
      |              ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   23 |              +c2*f2*((a2+d2+b2+e2)-(c2+f2)))
      |              ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   24 |             -(a2*e2*f2+d2*e2*f2+c2*d2*e2+a2*b2*c2))/12.0000000000L;
      |             ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/include/features.h:523,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/os_defines.h:39,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/c++config.h:683,
                 from /usr/include/c++/14/bits/requires_hosted.h:31,
                 from /usr/include/c++/14/iostream:38,
                 from a.cc:1:
/usr/include/x86_64-linux-gnu/bits/mathcalls.h:176:1: note: candidate: 'double sqrt(double)'
  176 | __MATHCALL (sqrt,, (_Mdouble_ __x));
      | ^~~~~~~~~~
In file included from a.cc:9:
/usr/include/c++/14/cmath:446:3: note: candidate: 'constexpr long double std::sqrt(long double)'
  446 |   sqrt(long double __x)
      |   ^~~~
/usr/include/c++/14/cmath:442:3: note: candidate: 'constexpr float std::sqrt(float)'
  442 |   sqrt(float __x)
      |   ^~~~
a.cc: In function 'int main()':
a.cc:34:29: error: no match for 'operator>>' (operand types are 'std::istream' {aka 'std::basic_istream<char>'} and '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'})
   34 |     for(int i=0;i<N;i++)cin >> a[i];
In file included from /usr/include/c++/14/iostream:42:
/usr/include/c++/14/istream:170:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(bool&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  170 |       operator>>(bool& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:170:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:170:7: error: cannot bind non-const lvalue reference of type 'bool&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:174:7: note: candidate: 'std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(short int&) [with _CharT = char; _Traits = std::char_traits<char>]' (near match)
  174 |       operator>>(short& __n);
      |       ^~~~~~~~
/usr/include/c++/14/istream:174:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:174:7: error: cannot bind non-const lvalue reference of type 'short int&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:177:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(short unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  177 |       operator>>(unsigned short& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:177:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:177:7: error: cannot bind non-const lvalue reference of type 'short unsigned int&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:181:7: note: candidate: 'std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(int&) [with _CharT = char; _Traits = std::char_traits<char>]' (near match)
  181 |       operator>>(int& __n);
      |       ^~~~~~~~
/usr/include/c++/14/istream:181:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:181:7: error: cannot bind non-const lvalue reference of type 'int&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:184:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  184 |       operator>>(unsigned int& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:184:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:184:7: error: cannot bind non-const lvalue reference of type 'unsigned int&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:188:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  188 |       operator>>(long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:188:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:188:7: error: cannot bind non-const lvalue reference of type 'long int&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:192:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  192 |       operator>>(unsigned long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:192:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:192:7: error: cannot bind non-const lvalue reference of type 'long unsigned int&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:199:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long long int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  199 |       operator>>(long long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:199:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:199:7: error: cannot bind non-const lvalue reference of type 'long long int&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:203:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long long unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  203 |       operator>>(unsigned long long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:203:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:203:7: error: cannot bind non-const lvalue reference of type 'long long unsigned int&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:219:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(float&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  219 |       operator>>(float& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:219:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:219:7: error: cannot bind non-const lvalue reference of type 'float&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:223:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(double&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  223 |       operator>>(double& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:223:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:223:7: error: cannot bind non-const lvalue reference of type 'double&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:227:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long double&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  227 |       operator>>(long double& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:227:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:227:7: error: cannot bind non-const lvalue reference of type 'long double&' to a value of type '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'}
/usr/include/c++/14/istream:328:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(void*&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]'
  328 |       operator>>(void*& __p)
      |       ^~~~~~~~
/usr/include/c++/14/istream:328:25: note:   no known conversion for argument 1 from '__gnu_cxx::__alloc_traits<std::allocator<__float128>, __float128>::value_type' {aka '__float128'} to 'void*&'
  328 |       operator>>(void*& __p)
      |                  ~~~~~~~^~~
/usr/include/c++/14/istream:122:7: note: candidate: 'std::basic_istream<_CharT, _Traits>: