Language: C++

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=5003,INF=1<<30;

int main(){

    int N;cin>>N;
    vector<pair<ll,ll>> P(N);
    for(int i=0;i<N;i++){
        cin>>P[i].first>>P[i].second;
    }
    
    sort(all(P),[&](int i,int j){
        return atan2(double(P[i].first),double(P[i].second))<atan2(double(P[j].first),double(P[j].second));
    });
    
    vector<ll> xsum(N+1,0.0),ysum(N+1,0.0);
    ll ans=0;
    
    for(int i=1;i<=N;i++){
        xsum[i]+=xsum[i-1]+P[i].first;
        ysum[i]+=ysum[i-1]+P[i].second;
    }
    
    for(int i=0;i<N;i++){
        for(int j=0;j<N;j++){
            ll X=0,Y=0;
            if(i<=j){
                X+=xsum[j+1]-xsum[i];
                Y+=ysum[j+1]-ysum[i];
            }else{
                X+=xsum[N]-(xsum[i+1]-xsum[j]);
                Y+=ysum[N]-(ysum[i+1]-ysum[j]);
            }
            ans=max(ans,X*X+Y*Y);
        }
    }
    
    long double left=0.0,right=2000000000.0,mid;
    for(int i=0;i<300;i++){
        mid=(left+right)/2.0;
        if(mid*mid>=ans) right=mid;
        else left=mid;
    }
    
    cout<<setprecision(25)<<mid<<endl;
}




Compiler output:
In file included from /usr/include/c++/14/bits/stl_algobase.h:71,
                 from /usr/include/c++/14/algorithm:60,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:51,
                 from a.cc:1:
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'constexpr bool __gnu_cxx::__ops::_Iter_comp_iter<_Compare>::operator()(_Iterator1, _Iterator2) [with _Iterator1 = __gnu_cxx::__normal_iterator<std::pair<long long int, long long int>*, std::vector<std::pair<long long int, long long int> > >; _Iterator2 = __gnu_cxx::__normal_iterator<std::pair<long long int, long long int>*, std::vector<std::pair<long long int, long long int> > >; _Compare = main()::<lambda(int, int)>]':
/usr/include/c++/14/bits/stl_algo.h:1777:14:   required from 'void std::__insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
 1777 |           if (__comp(__i, __first))
      |               ~~~~~~^~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1817:25:   required from 'void std::__final_insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
 1817 |           std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1908:31:   required from 'void std::__sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
 1908 |           std::__final_insertion_sort(__first, __last, __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:4805:18:   required from 'void std::sort(_RAIter, _RAIter, _Compare) [with _RAIter = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = main()::<lambda(int, int)>]'
 4805 |       std::__sort(__first, __last, __gnu_cxx::__ops::__iter_comp_iter(__comp));
      |       ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:15:9:   required from here
   15 |     sort(all(P),[&](int i,int j){
      |     ~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
   16 |         return atan2(double(P[i].first),double(P[i].second))<atan2(double(P[j].first),double(P[j].second));
      |         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   17 |     });
      |     ~~   
/usr/include/c++/14/bits/predefined_ops.h:158:30: error: no match for call to '(main()::<lambda(int, int)>) (std::pair<long long int, long long int>&, std::pair<long long int, long long int>&)'
  158 |         { return bool(_M_comp(*__it1, *__it2)); }
      |                       ~~~~~~~^~~~~~~~~~~~~~~~
a.cc:15:17: note: candidate: 'main()::<lambda(int, int)>'
   15 |     sort(all(P),[&](int i,int j){
      |                 ^
a.cc:15:17: note:   no known conversion for argument 1 from 'std::pair<long long int, long long int>' to 'int'
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'bool __gnu_cxx::__ops::_Val_comp_iter<_Compare>::operator()(_Value&, _Iterator) [with _Value = std::pair<long long int, long long int>; _Iterator = __gnu_cxx::__normal_iterator<std::pair<long long int, long long int>*, std::vector<std::pair<long long int, long long int> > >; _Compare = main()::<lambda(int, int)>]':
/usr/include/c++/14/bits/stl_algo.h:1757:20:   required from 'void std::__unguarded_linear_insert(_RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Val_comp_iter<main()::<lambda(int, int)> >]'
 1757 |       while (__comp(__val, __next))
      |              ~~~~~~^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1785:36:   required from 'void std::__insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
 1785 |             std::__unguarded_linear_insert(__i,
      |             ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~
 1786 |                                 __gnu_cxx::__ops::__val_comp_iter(__comp));
      |                                 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1817:25:   required from 'void std::__final_insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
 1817 |           std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1908:31:   required from 'void std::__sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
 1908 |           std::__final_insertion_sort(__first, __last, __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:4805:18:   required from 'void std::sort(_RAIter, _RAIter, _Compare) [with _RAIter = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = main()::<lambda(int, int)>]'
 4805 |       std::__sort(__first, __last, __gnu_cxx::__ops::__iter_comp_iter(__comp));
      |       ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:15:9:   required from here
   15 |     sort(all(P),[&](int i,int j){
      |     ~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
   16 |         return atan2(double(P[i].first),double(P[i].second))<atan2(double(P[j].first),double(P[j].second));
      |         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   17 |     });
      |     ~~   
/usr/include/c++/14/bits/predefined_ops.h:240:30: error: no match for call to '(main()::<lambda(int, int)>) (std::pair<long long int, long long int>&, std::pair<long long int, long long int>&)'
  240 |         { return bool(_M_comp(__val, *__it)); }
      |                       ~~~~~~~^~~~~~~~~~~~~~
a.cc:15:17: note: candidate: 'main()::<lambda(int, int)>'
   15 |     sort(all(P),[&](int i,int j){
      |                 ^
a.cc:15:17: note:   no known conversion for argument 1 from 'std::pair<long long int, long long int>' to 'int'
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'bool __gnu_cxx::__ops::_Iter_comp_val<_Compare>::operator()(_Iterator, _Value&) [with _Iterator = __gnu_cxx::__normal_iterator<std::pair<long long int, long long int>*, std::vector<std::pair<long long int, long long int> > >; _Value = std::pair<long long int, long long int>; _Compare = main()::<lambda(int, int)>]':
/usr/include/c++/14/bits/stl_heap.h:140:48:   required from 'void std::__push_heap(_RandomAccessIterator, _Distance, _Distance, _Tp, _Compare&) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Distance = long int; _Tp = pair<long long int, long long int>; _Compare = __gnu_cxx::__ops::_Iter_comp_val<main()::<lambda(int, int)> >]'
  140 |       while (__holeIndex > __topIndex && __comp(__first + __parent, __value))
      |                                          ~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_heap.h:247:23:   required from 'void std::__adjust_heap(_RandomAccessIterator, _Distance, _Distance, _Tp, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Distance = long int; _Tp = pair<long long int, long long int>; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
  247 |       std::__push_heap(__first, __holeIndex, __topIndex,
      |       ~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  248 |                        _GLIBCXX_MOVE(__value), __cmp);
      |                        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_heap.h:356:22:   required from 'void std::__make_heap(_RandomAccessIterator, _RandomAccessIterator, _Compare&) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
  356 |           std::__adjust_heap(__first, __parent, __len, _GLIBCXX_MOVE(__value),
      |           ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  357 |                              __comp);
      |                              ~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1593:23:   required from 'void std::__heap_select(_RandomAccessIterator, _RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<long long int, long long int>*, vector<pair<long long int, long long int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(int, int)> >]'
 1593 |       std::__make_heap(__first, __middle, __comp);
      |       ~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
/us