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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))",
]