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 debug import debug
from bisect import *
import sys; input = sys.stdin.readline
n, m, k = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))

aa, bb = [], []
i = 0
while i < n:
	v = i
	while i < n and a[i] == 1: i+=1
	vv = i-1
	if vv >= v: aa.append(vv-v+1)
	i+=1

i = 0
while i < m:
	v = i
	while i < m and b[i] == 1: i+=1
	vv = i-1
	if vv >= v: bb.append(vv-v+1)
	i+=1
aa.sort()
bb.sort()
n1, n2 = len(aa), len(bb)
div, ans = 1, 0
while div*div <= k:
	if k%div == 0:
		q = k//div
		i1 = bisect_left(aa, div)
		i2 = bisect_left(bb, q)
		r, w = 0, 0
		for i in range(i1, n1): r += aa[i] - div + 1
		for i in range(i2, n2): w += bb[i] - q + 1
		ans += r*w
		if q != div:
			i1 = bisect_left(aa, q)
			i2 = bisect_left(bb, div)
			r, w = 0, 0
			for i in range(i1, n1): r += aa[i] - q + 1
			for i in range(i2, n2): w += bb[i] - div + 1
			ans += r*w
	div += 1
print(ans)