import PABCSystem

pi = 3.14159265358979

def sqrt(x: float) -> float:
    return PABCSystem.Sqrt(x)

def trunc(x: float) -> int:
    return PABCSystem.Trunc(x)

def floor(x: float) -> int:
    return PABCSystem.Floor(x)
    
def ceil(x: float) -> int:
    return PABCSystem.Ceil(x)

def log(x: float) -> float:
    return PABCSystem.Log(x)

def log1p(x: float) -> float:
    return PABCSystem.Log(1+ x)

def log2(x: float) -> float:
    return PABCSystem.Log2(x)

def log10(x: float) -> float:
    return PABCSystem.Log10(x)
    
def log(x: float, base: int) -> float:
    return PABCSystem.LogN(base, x)

def exp(x: float) -> float:
    return PABCSystem.Exp(x)

def expm1(x: float) -> float:
    return PABCSystem.Exp(x - 1)

def exp2(x: float) -> float:
    return PABCSystem.Exp(log(2) * x)

def sin(x: float) -> float:
    return PABCSystem.Sin(x)

def sinh(x: float) -> float:
    return PABCSystem.Sinh(x)

def cos(x: float) -> float:
    return PABCSystem.Cos(x)

def cosh(x: float) -> float:
    return PABCSystem.Cosh(x)

def tan(x: float) -> float:
    return PABCSystem.Tan(x)
    
def tanh(x: float) -> float:
    return PABCSystem.Tanh(x)
    
def acos(x: float) -> float:
    return PABCSystem.ArcCos(x)

def asin(x: float) -> float:
    return PABCSystem.ArcSin(x)

def atan(x: float) -> float:
    return PABCSystem.ArcTan(x)

def atan2(y: float, x: float) -> float:
    return PABCSystem.ArcTan(y / x)

def pow(x: float, y: int) -> float:
    return PABCSystem.Power(x, y)

def cbrt(x: float) -> float:
    return pow(x, 1/3)

def fabs(x: float) -> float:
    return PABCSystem.Abs(x)

def pow(x: float, y: float) -> float:
    return PABCSystem.Power(x, y)

def isqrt(x: int) -> int:
    return floor(sqrt(x))

def remainder(x: int, y: int) -> int:
    return x - (x // y) * y
    
def factorial(n: int) -> int:
    if n == 0:
        return 1
    return n * factorial(n - 1)
    
def perm(n: int, k: int) -> int:
    return factorial(n) // factorial(n - k)

def comb(n: int, k: int) -> int:
    return perm(n, k) // factorial(k)