cases = [ 
   "((10 / x) / 1 / 1 + 100) + (2 * 100)",
    "((10 / x) / 1 / 1 + 100) ^ (-(10 + 2) + 1 / 1 + 1 / 1)",
    "((10 / x) / 1 / 1 + 100)",
    "((10 / x) / 1 / 1 ^ (10 / x) - 2 - 1 ^ 10)",
    "(-(10 + 2) + 1 / 1 + 1 / 1)",
    "(-1 * (10 / x) / 1 / 1 + (10 + 2))",
    "(-2 + -100)",
    "(1 - (10 / x) / 1 / 1 + (10 + 2))",
    "(1 / 1 + 1 / 1 + (10 + 2) / 100 * (10 + 2) / (10 + 2) - (10 / x)) / 10 - x * (10 / x) / -1",
    "(1 / 1 + 1 / 1 + (10 + 2) / 100 * (10 + 2) / (10 + 2) - (10 / x)) ^ (2 * 5) * -1 ^ 10",
    "(1 / 1 + 1 / 1 + (10 + 2) / 100 * (10 + 2) / (10 + 2) - (10 / x))",
    "(1 / 1 + 1 / 1 + 2 / 1 ^ 10 * (2 * 100) - --1)",
    "(1 / 1 + 2 + 1) * 0",
    "(1 / 1 + 2 + 1)",
    "(1 / 1 + 2 - 10 - x * (10 / x) - (10 / x))",
    "(1 / 1 + 2 / ((10 / x) / 1 / 1 ^ (10 / x) - 2 - 1 ^ 10)) ^ -1 ^ 10",
    "(1 / 1 + 2 / ((10 / x) / 1 / 1 ^ (10 / x) - 2 - 1 ^ 10))",
    "(1 ^ 10 ^ (10 + 2) - (10 / x))",
    "(10 + (1 / 1 + 1 / 1 + (10 + 2) / 100 * (10 + 2) / (10 + 2) - (10 / x)))",
    "(10 + 2) - (10 / x)",
    "(10 + 2) - -1",
    "(10 + 2)",
    "(10 - x * (10 / x) - (10 / x) * -1)",
    "(10 / x) * 10 - x * (10 / x) - (10 / x)",
    "(10 / x) - 2",
    "(10 / x) / 1 / 1 + (10 + 2) / (2 * 100) / -2 / (10 / x) / 1 / 1 + (10 + 2)",
    "(10 / x) / 1 / 1 + (10 + 2) / (2 * 100)",
    "(10 / x) / 1 / 1 + (10 + 2)",
    "(10 / x) / 1 / 1 ^ (10 / x) - 2 / (10 + 2) / -10 - x",
    "(10 / x) / 1 / 1 ^ (10 / x) - 2 / (10 + 2)",
    "(10 / x) / 1 / 1 ^ (10 / x) - 2",
    "(10 / x) / 1 / 1",
    "(10 / x)",
    "(2 * 100) * -1 ^ 10",
    "(2 * 100)",
    "(x ^ -10 * 100)",
    "-((10 / x) / 1 / 1 + 100)",
    "-(10 + 2)",
    "--1 - (1 / 1 + 2 / ((10 / x) / 1 / 1 ^ (10 / x) - 2 - 1 ^ 10))",
    "--1",
    "--2",
    "-0 / 1 / 1 + 1 / 1 + 2",
    "-1 - (1 / 1 + 2 / ((10 / x) / 1 / 1 ^ (10 / x) - 2 - 1 ^ 10)) - (2 * 100)",
    "-1 - (1 / 1 + 2 / ((10 / x) / 1 / 1 ^ (10 / x) - 2 - 1 ^ 10))",
    "-1 / 1 + 1 / 1 + 2",
    "-1 / 1 + 2",
    "-1 ^ 10",
    "-1",
    "-10 * 100",
    "-10",
    "-100 - 1 / 1 + 1 / 1 + (10 + 2) - 10 - x * (10 / x) / -1 / (10 / x) / 1 / 1 ^ (10 / x) - 2 / (10 + 2)",
    "-100 - 1 / 1 + 1 / 1 + (10 + 2)",
    "-100",
    "-2 / (10 / x) / 1 / 1 + (10 + 2)",
    "-2",
    "0 / 1 / 1 + 1 / 1 + 2",
    "0",
    "1 / 1 + 1 / 1 + (10 + 2) / (10 / x) / 1 / 1 + (10 + 2) / (2 * 100)",
    "1 / 1 + 1 / 1 + (10 + 2)",
    "1 / 1 + 1 / 1 + 2 / (10 / x) * 10 - x * (10 / x) - (10 / x)",
    "1 / 1 + 1 / 1 + 2 / 1 ^ 10 * (2 * 100)",
    "1 / 1 + 1 / 1 + 2 / 1 ^ 10 + (10 / x) / 1 / 1 + (10 + 2) / (2 * 100)",
    "1 / 1 + 1 / 1 + 2 / 1 ^ 10",
    "1 / 1 + 1 / 1 + 2",
    "1 / 1 + 1 / 1 / 10 - x * (10 / x) / -1 + (10 + (1 / 1 + 1 / 1 + (10 + 2) / 100 * (10 + 2) / (10 + 2) - (10 / x)))",
    "1 / 1 + 1 / 1 / 10 - x * (10 / x) / -1",
    "1 / 1 + 1 / 1",
    "1 / 1 + 2",
    "1 / 1",
    "1 ^ 10",
    "1",
    "10 - x * (10 / x) - (10 / x)",
    "10 - x * (10 / x) / -1 / (10 / x) / 1 / 1 ^ (10 / x) - 2 / (10 + 2)",
    "10 - x * (10 / x) / -1",
    "10 - x * (10 / x)",
    "10",
    "100 * (10 + 2) / (10 + 2) - (10 / x)",
    "100 * (10 + 2)",
    "100",
    "2 + -10 * 100 + 10 - x * (10 * x) - (10 * x)",
    "2 + -10 * 100",
    "2",
    "x^3 - x - 2",
    "(x - 1)*(x - 3)",
    "(x - 4)*(x - 5)*(x - 6)",
    "(x - 7)*(x - 8)*(x - 9)*(x - 10)",
    "(x - 1)*(x - 3)",
    "x^3 - x^2 + 2*x",
    "x^3 - x + 2",
    "x^2 -13",
    "(x + 4)^2 - 16",
    "-2* w^2 -6*sqrt(3)*w + 108",
    "(y + 4)^ - 1225",
    "(v-2)^2 - 1764",
    "q^2 - 9*q + 20",
    "-2*m^2 + 10*m - 12",
    "4*q^2 - 24*q + 20",
    "x^2 - 8",
    "-5*a^2 - 30*sqrt(7) * a - 280",
    "x^2 - 20",
    "-2*n^2 + 12 * n - 18",
    "-4 * x^2 - 32 * sqrt(3) * x - 8",
    "4 * x^2 - 24 * x + 32",
    "(x-3)^2 - 4",
]

cases_extend = [
    "(10 + 2) - (10 / x) ^ 100 * (10 + 2) / (10 + 2) - (10 / x)",
    "-1 / 1 + 2 ^ 10 - x",
    "-10 - x",
    "10 - x",
    "x",
    "100 * (10 + 2) + (x ^ -10 * 100)",
    "100 * (10 + 2) / (10 + 2) - (10 / x) / (1 / 1 + 2 - 10 - x * (10 / x) - (10 / x))",
]