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 = list(map(int, input().split()))
a = list(map(int, input().split()))
b = list(map(int, input().split()))
k_div = []
count = 1
for i in range(int(n[2] ** (1/2))):
    if n[2] % count == 0:
        k_div.append(count)
    count += 1
for i in range(len(k_div)):
    if k_div[i] ** 2 != n[2]:
        k_div.append(int(n[2]/k_div[i]))
gra = {}
grb = {}
c = 0
d = 0
for i in range(n[0]):
    if a[i] == 1:
        c += 1
    else:
        if c != 0:
            gra[c] = gra.get(c, 0) + 1
            c = 0
if c > 0:
    gra[c] = gra.get(c, 0) + 1
for i in range(n[1]):
    if b[i] == 1:
        d += 1
    else:
        if d != 0:
            grb[d] = grb.get(d, 0) + 1
            d = 0
if d > 0:
    grb[d] = grb.get(d, 0) + 1
rect = 0
for i in range(len(k_div)):
    row = 0
    column = 0
    for key in gra.keys():
        if key >= k_div[i]:
            row += (key - k_div[i] + 1) * gra[key]
    for key in grb.keys():
        if key >= n[2] / k_div[i]:
            column += (key - n[2] / k_div[i] + 1) * grb[key]
    rect += int(row * column)
print(rect)
