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>
import sys
input = sys.stdin.readline

n, m, k = map(int, input().split())
factors = set()
for i in range(1, int(k**0.5) + 3):
    if k % i == 0:
        factors.add(i)
        factors.add(k // i)

x = [*map(int, input().split())]
y = [*map(int, input().split())]

con_x = [0]*n
i = 0
while i < n:
    if x[i]:
        a = 0
        while i + a < n and x[i+a]:
            a += 1
        b = a
        for p in range(i, i + a):
            con_x[p] = b
            b -= 1
        i = i + a
    else:
        i += 1
con_y = [0]*m
i = 0
while i < m:
    if y[i]:
        a = 0
        while i + a < m and y[i+a]:
            a += 1
        b = a
        for p in range(i, i + a):
            con_y[p] = b
            b -= 1
        i = i + a
    else:
        i += 1

ans = 0
for p in factors:
    q = k // p
    if p > n or q > m:
        continue
    c = 0
    for i in range(n-p+1):
        if con_x[i] >= p:
            c += 1
    if c:
        d = 0
        for j in range(m - q + 1):
            if con_y[j] >= q:
                d += 1
        ans += c*d
print(ans)

