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 = [int(i) for i in input().split()]
b = [int(i) for i in input().split()]
# перепутал a и b, поэтому меняю их местами:
a, b = b, a


def search_for_divisors(num):
    i = 1
    while i * i <= num:
        if num % i == 0:
            divisors.append([i, num // i])
            if i != num // i:
                divisors.append([num // i, i])
        i += 1


divisors = []
search_for_divisors(k)

breadth = {}
ones = 0
for a_i in a + [0]:
    if a_i == 1:
        ones += 1
    else:
        if ones not in breadth:
            breadth[ones] = 1
        else:
            breadth[ones] += 1
        ones = 0

height = {}
ones = 0
for b_i in b + [0]:
    if b_i == 1:
        ones += 1
    else:
        if ones not in height:
            height[ones] = 1
        else:
            height[ones] += 1
        ones = 0

# print(breadth)
# print(height)

subrectangles = {}
for a_i in breadth:
    for b_i in height:
        subrectangles[a_i, b_i] = breadth[a_i] * height[b_i]

# print(divisors)
# print(subrectangles)

total_capacity = 0
for the_size_of_the_rectangle in divisors:
    for borders in subrectangles:
        if the_size_of_the_rectangle[0] <= borders[0] and the_size_of_the_rectangle[1] <= borders[1]:
            total_capacity += (borders[0] - the_size_of_the_rectangle[0] + 1) * (borders[1] - the_size_of_the_rectangle[1] + 1) * subrectangles[borders]

print(total_capacity)
