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 math import sqrt
n, m, k = map(int, input().split())

a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

ac = [0] * (n + 1)
bc = [0] * (m + 1)

cs = 0

for ai in a:
    if ai == 1:
        cs += 1
    if ai == 0:
        ac[cs] += 1
        cs = 0
ac[cs] += 1

cs = 0
for bi in b:
    if bi == 1:
        cs += 1
    if bi == 0:
        bc[cs] += 1
        cs = 0
bc[cs] += 1

pairs = []

for i in range(1, int(sqrt(k) + 1)):
    if k % i == 0:
        pairs.append((i, k // i))

total = 0

for i, j in pairs:
    if i <= n and j <= m:
        act = 0
        for k in range(i, n + 1):
            act += ac[k] * (k - i + 1)
        bct = 0
        for k in range(j, m + 1):
            bct += bc[k] * (k - j + 1)

        total += act * bct
    if j <= n and i <= m and i != j:
        act = 0
        for k in range(j, n + 1):
            act += ac[k] * (k - j + 1)
        bct = 0
        for k in range(i, m + 1):
            bct += bc[k] * (k - i + 1)

        total += act * bct

print(total)
