#include <cmath>
#include <utility>
using namespace std;

int NOD(int a, int b) {
    a = abs(a);
    b = abs(b);
    while (a && b) {
        if (a > b) {
            a %= b;
        } else {
            b %= a;
        }
    }
    return a + b;
}

class Rational {
private:
    int num = 0;
    int den = 1;

public:
    Rational() {}

    Rational(int num, int den) {
        if (den < 0) {
            num *= -1;
            den *= -1;
        }
        int nod = NOD(num, den);
        num /= nod;
        den /= nod;
        this->num = num;
        this->den = den;
    }

    Rational(int num) {
        this->num = num;
        this->den = 1;
    }

    int numerator() const {
        return num;
    }

    int denominator() const {
        return den;
    }

    Rational& reduce() {
        if (den < 0) {
            num *= -1;
            den *= -1;
        }
        int nod = NOD(num, den);
        num /= nod;
        den /= nod;
        return *this;
    }

    Rational& operator += (const Rational& rat) {
        Rational r;
        r.num = num * rat.denominator() + den * rat.numerator();
        r.den = den * rat.denominator();
        *this = move(r);
        this->reduce();
        return *this;
    }

    Rational& operator -= (const Rational& rat) {
        Rational r;
        r.num = num * rat.denominator() - den * rat.numerator();
        r.den = den * rat.denominator();
        *this = move(r);
        this->reduce();
        return *this;
    }

    Rational& operator *= (const Rational& rat) {
        num *= rat.numerator();
        den *= rat.denominator();
        this->reduce();
        return *this;
    }

    Rational& operator /= (const Rational& rat) {
        int old_num = rat.numerator();
        int old_den = rat.denominator();
        num *= old_den;
        den *= old_num;
        this->reduce();
        return *this;
    }

    Rational& operator ++() {
        num += den;
        this->reduce();
        return *this;
    }

    Rational operator ++(int) {
        Rational r = *this;
        ++(*this);
        return r;
    }

    Rational& operator --() {
        num -= den;
        this->reduce();
        return *this;
    }

    Rational operator --(int) {
        Rational r = *this;
        --(*this);
        return r;
    }

    Rational operator + () const {
        return *this;
    }

    Rational operator - () const {
        Rational result(-num, den);
        return result;
    }
};

bool operator == (const Rational& rat1, const Rational& rat2) {
    return ((rat1.numerator() == rat2.numerator()) && (rat1.denominator() == rat2.denominator()));
}

bool operator != (const Rational& rat1, const Rational& rat2) {
    return ((rat1.numerator() != rat2.numerator()) || (rat1.denominator() != rat2.denominator()));
}

Rational operator + (const Rational& rat1, const Rational& rat2) {
    Rational result = rat1;
    return result += rat2;
}

Rational operator - (const Rational& rat1, const Rational& rat2) {
    Rational result = rat1;
    return result -= rat2;
}

Rational operator * (const Rational& rat1, const Rational& rat2) {
    Rational result = rat1;
    return result *= rat2;
}

Rational operator / (const Rational& rat1, const Rational& rat2) {
    Rational result = rat1;
    return result /= rat2;
}

#include <vector>
#include <iostream>

void printv(std::vector<Rational> v) {
    for (auto& i : v) {
        std::cout << i.numerator() << "/" << i.denominator() << " ";
    }
    std::cout << '\n';
}

Rational pr(std::vector<Rational> v1, std::vector<Rational> v2) {
    Rational ans = 0;
    for (int i = 0; i < v1.size(); ++i) {
        ans += v1[i] * v2[i];
    }
    return ans;
}

std::vector<Rational> sc(Rational r, std::vector<Rational> v) {
    for (auto& i : v) {
        i *= r;
    }
    return v;
}

std::vector<Rational> minu(std::vector<Rational> v1, std::vector<Rational> v2) {
    for (int i = 0; i < v1.size(); ++i) {
        v1[i] -= v2[i];
    }
    return v1;
}

std::vector<Rational> g_smitd(std::vector<Rational> v1, std::vector<Rational> v2) {
    return sc((pr(v1, v2) / pr(v1, v1)), v1);
}

void prn(Rational r) {
    std::cout << r.numerator() << "/" << r.denominator() << ' ';
}

int main() {
    std::vector<Rational> v1 = { 4, -1, -2, -2 };
    std::vector<Rational> v2 = { 0, 1, 0, 0 };
    std::vector<Rational> v3 = { 0, 0, 1, 0 };
    std::vector<Rational> v4 = { 0, 0, 0, 1 };
    v2 = minu(v2, g_smitd(v1, v2));
    auto v5 = minu(minu(v3, g_smitd(v1, v3)), g_smitd(v2, v3));
    v3 = v5;
    auto v6 = minu(minu(minu(v4, g_smitd(v1, v4)), g_smitd(v2, v4)), g_smitd(v3, v4));
    v4 = v6;
    prn(pr(v1, v1));
    std::cout << '\n';
    prn(pr(v2, v2));
    std::cout << '\n';
    prn(pr(v3, v3));
    std::cout << '\n';
    prn(pr(v4, v4));
    std::cout << '\n';
}