long double f1(vector<long double> v) {
    assert(v.size() == 2);
    return 100.0 * sqr(v[1] - sqr(v[0])) + sqr(1.0 - v[0]);
}

long double f1x1(vector<long double> v) {
    assert(v.size() == 2);
    return 2.0 * (200.0 * pow(v[0], 3) - 200.0 * v[0] * v[1] + v[0] - 1.0);
}

long double f1x2(vector<long double> v) {
    assert(v.size() == 2);
    return 200.0 * (v[1] - sqr(v[0]));
}

long double f1x1x1(vector<long double> v) {
    assert(v.size() == 2);
    return 1200.0 * sqr(v[0]) - 400.0 * v[1] + 2.0;
}

long double f1x1x2(vector<long double> v) {
    assert(v.size() == 2);
    return -400.0 * v[0];
}

long double f1x2x2(vector<long double> v) {
    assert(v.size() == 2);
    return 200.0;
}

long double f2(vector<long double> v) {
    assert(v.size() == 2);
    return sqr(v[0] - 4) + 4 * sqr(v[1] - 2);
}

long double f2x1(vector<long double> v) {
    assert(v.size() == 2);
    return 2.0 * (v[0] - 4.0);
}

long double f2x2(vector<long double> v) {
    assert(v.size() == 2);
    return 8.0 * (v[1] - 2.0);
}

long double f2x1x1(vector<long double> v) {
    assert(v.size() == 2);
    return 2.0;
}

long double f2x1x2(vector<long double> v) {
    assert(v.size() == 2);
    return 0;
}

long double f2x2x2(vector<long double> v) {
    assert(v.size() == 2);
    return 8.0;
}

long double f3(vector<long double> v) {
    assert(v.size() == 2);
    return sqr(v[0] - 2) + sqr(v[1] + 3);
}

long double f3x1(vector<long double> v) {
    assert(v.size() == 2);
    return 2.0 * (v[0] - 2.0);
}

long double f3x2(vector<long double> v) {
    assert(v.size() == 2);
    return 2.0 * (v[1] + 3.0);
}

long double f3x1x1(vector<long double> v) {
    assert(v.size() == 2);
    return 2.0;
}

long double f3x1x2(vector<long double> v) {
    assert(v.size() == 2);
    return 0;
}

long double f3x2x2(vector<long double> v) {
    assert(v.size() == 2);
    return 2.0;
}

long double f4(vector<long double> v) {
    assert(v.size() == 2);
    return sqr(v[0] - 3) + sqr(v[1]);
}