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>
# todo: wrong answer on test 3

def count_rectangles(a, b, area):
    a_lens = get_all_lengths(a)
    b_lens = get_all_lengths(b)
    result = 0
    for i in range(1, len(a_lens)):
        if area % i == 0 and area // i <= len(b):
            result += a_lens[i] * b_lens[area // i]
    return result


def get_all_lengths(x):
    lengths = [0 for _ in range(len(x) + 1)]
    i = 0
    while i < len(x):
        if x[i] == 0:
            i += 1
            continue

        j = i
        while j < len(x) and x[j] == 1:
            j += 1

        for length in range(1, j - i + 1):
            # compute amount of subsets of size len
            lengths[length] += (j - i) - length + 1
        i = j
    return lengths


if __name__ == "__main__":
    area = list(map(lambda x: int(x), input().strip().split()))[2]
    a = list(map(lambda x: int(x), input().strip().split()))
    b = list(map(lambda x: int(x), input().strip().split()))
    print(count_rectangles(a, b, area))
