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 = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))

a_lenths = {}
curr_len = 0
for i in range(len(a)):
	if a[i] == 1:
		curr_len += 1
	else:
		if curr_len in a_lenths:
			a_lenths[curr_len] += 1
		else:
			a_lenths[curr_len] = 1
		curr_len = 0
if curr_len != 0:
	if curr_len in a_lenths:
		a_lenths[curr_len] += 1
	else:
		a_lenths[curr_len] = 1

b_lenths = {}
curr_len = 0
for i in range(len(b)):
	if b[i] == 1:
		curr_len += 1
	else:
		if curr_len in b_lenths:
			b_lenths[curr_len] += 1
		else:
			b_lenths[curr_len] = 1
		curr_len = 0
if curr_len != 0:
	if curr_len in b_lenths:
		b_lenths[curr_len] += 1
	else:
		b_lenths[curr_len] = 1

# print("a_lenths", a_lenths)
# print("b_lenths", b_lenths)

k_divs = []
for i in range(1, int(k ** 0.5)+1):
	if k % i == 0:
		k_divs.append(i)
		if k // i != i:
			k_divs.append(k // i)

ans = 0
for seg_a in a_lenths:
	for div1 in k_divs:
		if div1 <= seg_a:
			div2 = k // div1
			num_seg_a = (seg_a - div1 + 1) * a_lenths[seg_a]
			for seg_b in b_lenths:
				if div2 <= seg_b:
					num_seg_b =  (seg_b - div2 + 1) * b_lenths[seg_b]
					ans += num_seg_a * num_seg_b
					# print("div1", div1)
					# print("div2", div2)
					# print("num_seg_a", num_seg_a)
					# print("num_seg_b", num_seg_b)
					# print("ans", ans)
print(ans)

