from math import sqrt
from math import degrees
from math import acos

class Vector:

    def __init__(self, lst):
        self.vec = tuple(lst)

    def __repr__(self):
        return str(self.vec)

    def __len__(self):
        return len(self.vec)

    def __eq__(self,vector):
        return self.vec == vector.vec and len(self) == len(vector)

    def __add__(self,vector):
        lst = [0]*len(self)
        if len(self) != len(vector):
            return None
        else:
            for i in range(0,len(self)):
                lst[i] = self.vec[i] + vector.vec[i]
        return Vector(lst)

    def __neg__(self):
        vector = [0]*len(self)
        for i in range(0,len(self)):
            vector[i] = self.vec[i]*-1
        return Vector(vector)

    def __sub__(self,vector):
        lst =[0]*len(self)
        if len(self) != len(vector):
            return None
        else:
            for i in range(0,len(self)):
                lst[i] = self.vec[i] + -vector.vec[i]
            return Vector(lst)

    def __mul__(self,vector):
        lst =[0]*len(self)
        if type(vector) is type(self):
            if len(self) != len(vector):
                return None
            for i in range(0,len(self)):
                lst[i] = self.vec[i] * vector.vec[i]
            return sum(lst)
        else:
            for i in range(0,len(self)):
                lst[i] = self.vec[i] * vector
        return Vector(lst)

    def __rmul__(self,vector):
        return self * vector

    def __getitem__(self,i):
        return self.vec[i]

    def norm(self):
        vector = self * self
        total = 0
        for i in range(0,len(vector)):
            total += vector.vec[i]
        return sqrt(total)

    def angle(self,vector):
        vect1 = self * vector
        vect2 = self.norm() * vector.norm()
        total = 0
        for i in range(0, len(vect1)):
            total += vect1.vec[i]
        return degrees(acos(total/vect2))