cases2 = [
    "0",
    "1",
    "2",
    "10",
    "100",
    "(10 + 2)",
    "1 / 1",
    "(10 / x)",
    "1 / 1 + 2",
    "(10 / x) / 1 / 1",
    "(10 / x) - 2",
    "(2 * 100)",
    "((10 / x) / 1 / 1 + 100)",
    "1 ^ 10",
    "-1 / 1 + 2",
    "10 - x * (10 / x)",
    "-1",
    "1 / 1 + 1 / 1 + 2",
    "100 * (10 + 2)",
    "(10 / x) / 1 / 1 ^ (10 / x) - 2",
    "(10 / x) / 1 / 1 ^ (10 / x) - 2 / (10 + 2)",
    "1 / 1 + 1 / 1",
    "10 - x * (10 / x) / -1",
    "1 / 1 + 1 / 1 + 2 / 1 ^ 10",
    "(1 / 1 + 2 + 1)",
    "(10 / x) / 1 / 1 + (10 + 2)",
    "10 - x * (10 / x) - (10 / x)",
    "1 / 1 + 1 / 1 + (10 + 2)",
    "(-1 * (10 / x) / 1 / 1 + (10 + 2))",
    "(10 + 2) - (10 / x)",
    "(1 / 1 + 2 - 10 - x * (10 / x) - (10 / x))",
    "(1 / 1 + 2 + 1) * 0",
    "((10 / x) / 1 / 1 + 100) * (10 / x) / 1 / 1 ^ (10 / x) - 2",
    "1 ^ 10 + ((10 / x) / 1 / 1 + 100) * (10 / x) / 1 / 1 ^ (10 / x) - 2",
    "1 / 1 + 2 ^ 10 - x * (10 / x) / -1",
    "(10 + 2) - (10 / x) * (10 / x) / 1 / 1 + (10 + 2)",
    "-1 / 1 + 2 - -1 / 1 + 2",
    "10 - x * (10 / x) - (10 / x) / 10 - x * (10 / x) - (10 / x) - 1 / 1 + 2 ^ 10 - x * (10 / x) / -1",
    "-1 / 1 + 2 - -1 / 1 + 2 - (2 * 100)",
    "0 / 1 / 1 + 1 / 1 + 2",
    "1 / 1 + 1 / 1 + 2 / 1 ^ 10 + (10 + 2) - (10 / x) * (10 / x) / 1 / 1 + (10 + 2)",
    "1 / 1 + 1 / 1 / 10 - x * (10 / x) / -1",
    "--1 / 1 + 2 - -1 / 1 + 2",
    "10 + -1 / 1 + 2",
    "-1 / 1 + 2 - -1 / 1 + 2 - (2 * 100) + 1 ^ 10",
    "(10 + 2) - (10 / x) - -1",
    "10 - x * (10 / x)",
    "(10 / x) / 1 / 1 + (10 + 2) - 1 / 1 + 1 / 1 + (10 + 2)",
    "1 ^ 10 * (2 * 100)",
    "---1 * 1 + 2 - -1 * 1 + 2",
    "(1 * 1 + 1 * 1 * 10 - x * (10 * x) * -1 + 100 - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1) * 10 - x * (10 * x) - (10 * x) - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1",
    "(1 * 1 + 1 * 1 * 10 - x * (10 * x) * -1 + 100 - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1) * 1 * 1 + 1 * 1 + 2",
    "10 + -1 * 1 + 2 - 10 - x * (10 * x) - (10 * x)",
    "1 * 1 + 2 ^ 10 - x * (10 * x) * -1 ^ (1 * 1 + 1 * 1 + (10 + 2) * 10 - x * (10 * x) - (10 * x) - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1)",
    "(1 * 1 + 1 * 1 * 10 - x * (10 * x) * -1 + 100 - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1) * 10 - x * (10 * x) - (10 * x) - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1 * (10 * x) - 2 * 1",
    "1 * 1 + 1 * 1 + 2 * 1 ^ 10 * (2 * 100)",
    "--1 * 1 + 2 - -1 * 1 + 2 + 100 - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1",
    "x - 10 - x * (10 * x) - (10 * x) * 10 - x * (10 * x) - (10 * x) - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1 * 10 - x * (10 * x) - (10 * x) - ((10 * x) * 1 * 1 + 100) * (10 * x) * 1 * 1 ^ (10 * x) - 2",
    "10 - x * (10 * x) + 10 - x * (10 * x) - (10 * x)",
    "((10 * x) * 1 * 1 + (10 + 2) - 1 * 1 + 1 * 1 + (10 + 2) * 10 - x * (10 * x) + 10 - x * (10 * x) - (10 * x))",
    "(10 + 2) - -1",
    "10 + -1 * 1 + 2 * 10 - x * (10 * x) * -1",
    "(--1 * 1 + 2 - -1 * 1 + 2 + 100 - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1 - (10 * x) * 1 * 1 ^ (10 * x) - 2 * 1 ^ 10 * (2 * 100) * (10 * x) * 1 * 1 ^ (10 * x) - 2 * (10 + 2))",
]

cases2_extend = [
    "((10 * x) * 1 * 1 + 100) ^ 1 * 1 + 1 * 1 + 2 * 1 ^ 10 * (2 * 100)",
    "(10 * x) * 1 * 1 ^ (10 * x) - 2 * 1 ^ 10 * (2 * 100)",
    "(10 * x) * 1 * 1 ^ (10 * x) - 2 * 1 ^ 10 * (2 * 100) * (10 * x) * 1 * 1 ^ (10 * x) - 2 * (10 + 2)",
    "(10 * x) * 1 * 1 ^ (10 * x) - 2 * (10 + 2) * 1 ^ 10 * (2 * 100)",
    "(10 * x) * 1 * 1 ^ (10 * x) - 2 * (10 + 2) * 1 ^ 10 * (2 * 100) - ((10 * x) * 1 * 1 + 100) * (10 * x) * 1 * 1 ^ (10 * x) - 2",
    "arctan(10 - x * (10 * x) * -1)",
    "10 - x * (10 * x) - (10 * x) * 10 - x * (10 * x) - (10 * x) - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1 * 10 - x * (10 * x) - (10 * x) - ((10 * x) * 1 * 1 + 100) * (10 * x) * 1 * 1 ^ (10 * x) - 2",
    "10 - x * (10 * x) - (10 * x) * 10 - x * (10 * x) - (10 * x) - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1 * (2 * 100)",
    "10 - x * (10 * x) - (10 * x) - ((10 * x) * 1 * 1 + 100) * (10 * x) * 1 * 1 ^ (10 * x) - 2",
    "10 - x * (10 * x) - (10 * x) * 10 - x * (10 * x) - (10 * x) - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1 * 10 - x * (10 * x) - (10 * x) - ((10 * x) * 1 * 1 + 100) * (10 * x) * 1 * 1 ^ (10 * x) - 2 * 1 * 1 + 1 * 1 + (10 + 2) * (10 + 2) - (10 * x) * (10 * x) * 1 * 1 + (10 + 2)",
    "x",
    "x - 10 + -1 / 1 + 2",
    "10 - x",
    "(10 - x * (10 / x) + (10 / x) - 2 * 1)",
    "e(e(x))",
    "e(e(x)) + (10 + 2) - (10 / x)",
    "(e(e(x)) * (10 / x) / 1 / 1 ^ (10 / x) - 2 * 1 ^ 10 * (2 * 100))",
    "(e(e(x)) * (10 / x) / 1 / 1 ^ (10 / x) - 2 * 1 ^ 10 * (2 * 100)) + (2 * 100)",
    "(e(e(x)) * 10 - x * (10 / x) + 10 - x * (10 / x) - (10 / x))",
    "arctan(x / 1 / 1 + 1 / 1 + 2)",
    "x - 10 - x * (10 / x) - (10 / x) / 10 - x * (10 / x) - (10 / x) - 1 / 1 + 2 ^ 10 - x * (10 / x) / -1 * 10 - x * (10 / x) - (10 / x) - ((10 / x) / 1 / 1 + 100) * (10 / x) / 1 / 1 ^ (10 / x) - 2 + arctan(x / 1 / 1 + 1 / 1 + 2)",
    "(10 - x * (10 / x) / ((10 / x) / 1 / 1 + 100))",
    "(1 / 1 + 1 / 1 + (10 + 2) / 10 - x * (10 / x) - (10 / x) - 1 / 1 + 2 ^ 10 - x * (10 / x) / -1)",
    "100 - 1 - 1 + 2 ^ 10 - x * (10 - x) - -1",
    "100 - 1 - 1 + 2 ^ 10 - x * (10 - x) - -1",
    "(-1 * 1 + 2 - -1 * 1 + 2 - (2 * 100) + 1 ^ 10 * (1 * 1 + 2 - 10 - x * (10 * x) - (10 * x)))",
    "1 * 1 + 1 * 1 + (10 + 2) * (10 + 2) - (10 * x) * (10 * x) * 1 * 1 + (10 + 2)",
    "(1 * 1 + 1 * 1 * 10 - x * (10 * x) * -1 + 100 - 1 * 1 + 2 ^ 10 - x * (10 * x) * -1)",
    "-1 * 1 + 2 - -1 * 1 + 2 - (2 * 100) + 10 - x * (10 * x)",
    "-1 * 1 + 2 - -1 * 1 + 2 * (10 * x) * 1 * 1 + (10 + 2)",
    "(10 * x) - 2 * 1",
    "(-1 * 1 + 2 - -1 * 1 + 2 + (-1 * 1 + 2 - -1 * 1 + 2 - (2 * 100) + 1 ^ 10 * (1 * 1 + 2 - 10 - x * (10 * x) - (10 * x))))",
    "arctan(0 * 1 * 1 + 1 * 1 + 2)",
    "((-1 * 1 + 2 - -1 * 1 + 2 + (-1 * 1 + 2 - -1 * 1 + 2 - (2 * 100) + 1 ^ 10 * (1 * 1 + 2 - 10 - x * (10 * x) - (10 * x)))) - -1 * 1 + 2)",
    "(10 - x * (10 / x) - (10 / x) * -1)",
    "10 - x * (10 / x) - (10 / x) - 1 / 1 + 2 ^ 10 - x * (10 / x) / -1",
]