You are given an array a of length n and array b of length m both consisting of only integers 0 and 1. Consider a matrix c of size n × m formed by following rule: c_{i, j} = a_i ⋅ b_j (i.e. a_i multiplied by b_j). It's easy to see that c consists of only zeroes and ones too.

How many subrectangles of size (area) k consisting only of ones are there in c?

A subrectangle is an intersection of a consecutive (subsequent) segment of rows and a consecutive (subsequent) segment of columns. I.e. consider four integers x_1, x_2, y_1, y_2 (1 ≤ x_1 ≤ x_2 ≤ n, 1 ≤ y_1 ≤ y_2 ≤ m) a subrectangle c[x_1 ... x_2][y_1 ... y_2] is an intersection of the rows x_1, x_1+1, x_1+2, ..., x_2 and the columns y_1, y_1+1, y_1+2, ..., y_2.

The size (area) of a subrectangle is the total number of cells in it.

Input

The first line contains three integers n, m and k (1 ≤ n, m ≤ 40 000, 1 ≤ k ≤ n ⋅ m), length of array a, length of array b and required size of subrectangles.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 1), elements of a.

The third line contains m integers b_1, b_2, …, b_m (0 ≤ b_i ≤ 1), elements of b.

Output

Output single integer — the number of subrectangles of c with size (area) k consisting only of ones.

Examples

Input


3 3 2
1 0 1
1 1 1


Output


4


Input


3 5 4
1 1 1
1 1 1 1 1


Output


14

Note

In first example matrix c is:

<image>

There are 4 subrectangles of size 2 consisting of only ones in it:

<image>

In second example matrix c is:

<image>
from math import sqrt
def gen_dzielniki(val):
	ret = list()
	for i in range(1, int(sqrt(val)) + 1):
		if(not (val % i)):
			ret.append(i)
	for i in range(int(sqrt(val)), 0, -1):
		if(not (val % i) and i * i != val):
			ret.append(val//i)
	return ret


def zamien(lista):
	ret = []
	last = -1
	for i in range(len(lista)):
		if lista[i] == 0 and i != 0 and lista[i-1] != 0:
			ret.append(i - last - 1)
			last = i
		elif lista[i] == 1 and i == len(lista) - 1:
			ret.append(i - last)
		elif lista[i] == 0:
			last = i
		else:
			pass
	ret2 = {}
	for u in ret:
		if not ret2.get(u):
			ret2[u] = 1
		else:
			ret2[u] += 1
	return ret2


n, m, k = list(map(int, input().split()))

dzielniki = gen_dzielniki(k)

def policz(a, b):
	# print(str(a) + ' ' + str(b) + " " + str(k))
	ans = 0
	for i in dzielniki:
		A = a - i
		B = b - k/i
		# print(A, B, i)
		if A < 0 or B < 0:
			continue 
		ans += (A + 1) * (B + 1)
	# print("wynik to " + str(ans))
	return ans

mapa = {}

A = list(map(int, input().split()))
B = list(map(int, input().split()))

A = zamien(A)
B = zamien(B)

ans = 0

for u in A:
	for v in B:
		ans += A[u] * B[v] * policz(u, v)

print(int(ans))
