Сортировки, Кузичкин 141 группа

#include <fstream>
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>

struct Student
{
  string F, I;
  int score[3];
  int fullScore()
  {
    return score[0] + score[1] + score[2];
  }
  double averageGeom()
  {
    return sqrt(score[0] * score[1] * score[2]);
  }
  bool pred(const Student& stud)
  {
    if (fullScore() < stud.fullScore()) return true;
    else if (fullScore() == stud.fullScore() && averageGeom() < stud.averageGeom()) return true;
    else if (averageGeom() == stud.averageGeom()) return false;
  }
};

vector<Student> initVector(ifstream& in)
{
  vector<Student> base;
  while (in.peek() != EOF)
  {
    Student stud;
    in >> stud.F >> stud.I;
    for (int i = 0; i < 3; ++i) in >> stud.score[i];
    base.push_back(stud);
  }
  return base;
}

void printVector(vector<Student> base, ofstream& out)
{
  for (Student stud : base)
  {
    out << stud.F << " " << stud.I << " ";
    for (int i = 0; i < 3; ++i) out << elem.score[i];
  }
}

int main()
{
  ifstream in("input.txt");
  ofstream out("output.txt");
  vector<Student> base = initVector(in);
  sort(base.begin(), base.end(), pred);
  printVector(base, out);
}

input.txt:
sidorov sergey 100 100 100
kuzichkin pavel 50 50 50
orlov daniil 90 90 90
imanov rauf 100 100 100
tihonov levan 84 87 99

output.txt:
kuzichkin pavel 50 50 50
tihonov levan 84 87 99
orlov daniil 90 90 90
imanov rauf 100 100 100
sidorov sergey 100 100 100