class Polynom:
	def __init__(self, coeffs):
		self.coeffs=coeffs
		self.deg=len(coeffs)-1

	def __add__(self, other):
		if type(other)==Polynom:
			h=[]
			if len(self.coeffs)>len(other.coeffs):
				u=len(self.coeffs)-len(other.coeffs)
				for j in range(len(other.coeffs)):
					k=self.coeffs[j]+other.coeffs[j]
					h.append(k)
				h.append(self.coeffs[len(self.coeffs)-1])
			if len(self.coeffs)<len(other.coeffs):
				u=len(other.coeffs)-len(self.coeffs)
				for i in range(len(self.coeffs)):
					k=self.coeffs[i]+other.coeffs[i]
					h.append(k)
				h.append(other.coeffs[len(other.coeffs)-1])
			return Polynom(h)
		else:
			print("Sorrrrrry")

	def __sub__(self, other):
		if type(other)==Polynom:
			h=[]
			if len(self.coeffs)>len(other.coeffs):
				for j in range(len(other.coeffs)):
					k=self.coeffs[j]-other.coeffs[j]
					h.append(k)
				h.append(self.coeffs[len(self.coeffs)-1])
			if len(self.coeffs)<len(other.coeffs):
				for i in range(len(self.coeffs)):
					k=self.coeffs[i]-other.coeffs[i]
					h.append(k)
				h.append(other.coeffs[len(other.coeffs)-1])
			if len(self.coeffs)==len(other.coeffs):
				for i in range(len(self.coeffs)):
					k=self.coeffs[i]-other.coeffs[i]
					h.append(k)
			return Polynom(h)
		else:
			print("Sorrrrrry")

	def __mul__(self, other):
		if type(other) in [float, int]:
			return Polynom(list(map(lambda x: x*other, self.coeffs)))
		else:
			if type(other)==Polynom:
				p=Polynom([])
				for i in range(len(self.coeffs)+1):
					new_coeffs=[]
					if i>0:
						for i in range(i):
							new_coeffs.append(0)
					for j in range(len(other.coeffs)):
						new_coeffs.append(self.coeffs[i]*other.coeffs[j])
					if i==0:
						p=Polynom(new_coeffs)
					else:
						p = p + Polynom(new_coeffs)
				new=[]
				for k in range(1, len(p.coeffs)):
					new.append(p.coeffs[k])
				return Polynom(new)
			else:
				print("Sorrrrrry")

	def __str__(self):
		result=""
		for i in range(self.deg+1):
			c=self.coeffs[-1-i]
			if c==0:
				continue
			elif c==1:
				result+= "+ x^{} ".format(self.deg - i)
			elif c==-1:
				result+= "- x^{} ".format(self.deg - i)
			elif c>0:
				result+= "+ {}*x^{} ".format(c, self.deg - i)
			elif c<0:
				result+= "- {}*x^{} ".format(-c, self.deg - i)
		return result.strip("+ ")

	def __neg__(self):
		return self*(-1)

	def __call__(self,x):
		result=0
		for i in range(self.deg + 1):
			result+=self.coeffs[i]*x**i
		return result

	def derivative(self):
		new_coeffs=[]
		for i in range(1, self.deg+1):
			new_coeffs.append(self.coeffs[i]*i)
		return Polynom(new_coeffs)
	def __bool__(self):
		if self.coeffs!=[]:
			return True
		else:
			return False
	def __divmod__(self, other):
		h = Polynom(list(self.coeffs))
		div_coeffs = []
		k=[]
		while h.deg>=other.deg:
			l=[]
			new_coeffs=[]
			if h.deg-other.deg>0:
				for i in range(h.deg-other.deg):
					new_coeffs.append(0)
			for j in range(other.deg + 1):
				new_coeffs.append(other.coeffs[j]*h.coeffs[h.deg])
			div_coeffs.append(h.coeffs[h.deg])
			h=h-Polynom(new_coeffs)
			for i in range(h.deg):
				l.append(h.coeffs[i])
			h=Polynom(list(l))
		div_coeffs=div_coeffs[::-1]
		k=Polynom(list(div_coeffs))
		return k, h


	def __floordiv__(self, other):
		return self.__divmod__(other)[0]

	def __mod__(self, other):
		return self.__divmod__(other)[1]



	def number_of_roots(self, a, b):
		p=self//gcd(self, self.derivative())
		p1, p2 = p, p.derivative()
		system=[p1, p2]
		while p2:
			p1, p2 = p2, p1%p2
			system.append(p2)
		system=system[:-1]
		list_a=[]
		list_b=[]
		for s in system:
			if s(a)!=0:
				list_a.append(s(a))
			if s(b)!=0:
				list_b.append(s(b))
		n_a=0
		n_b=0
		for i in range(len(list_a)-1):
			if list_a[i]*list_a[i+1]<0:
				n_a+=1
			if list_b[i]*list_b[i+1]<0:
				n_b+=1
		return n_a-n_b



def gcd(p1, p2):
	while p2:
		p1, p2 = p2, p1%p2
	return p1









#p1=Polynom([1,1])
p2=Polynom([1, -2, 1])
#print(p2)
#print(p1)
#print(p2.derivative())
#print(p2%p1)
#print(gcd(p2,p1))
p3=Polynom([2,0,1])
p4=Polynom([0,1,1])
p1 = Polynom([24, -50, 35, -10, 1])
print(p1)
print(p1.number_of_roots(0, 6))