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

a = ''.join(input().split(' '))
b = ''.join(input().split(' '))


a = a.split('0')
b = b.split('0')

result = 0

divs = []


i = 1
while i*i <= k:
	if k%i == 0:
		divs.append(i)
	i += 1

a_count = dict()
b_count = dict()

for div in divs:
	a_count[div] = 0
	b_count[div] = 0
	a_count[k//div] = 0
	b_count[k//div] = 0


for subset in a:
	l = len(subset)
	for div in divs:
		if div <= l:
			a_count[div] += l - div + 1
		if k//div <= l and div*div != k:
			a_count[k//div] += l - k//div + 1

for subset in b:
	l = len(subset)
	for div in divs:
		if div <= l:
			b_count[div] += l - div + 1
		if k//div <= l and div*div != k:
			b_count[k//div] += l - k//div + 1

for div in divs:
	result += a_count[div]*b_count[k//div]
	if div*div != k:
		result += b_count[div]*a_count[k//div]

print(result)

