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())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
cnta = [0] * (n+1)
cntb = [0] * (m+1)

cnt = 0
for i in range(n+1):
    if i == n or a[i] == 0:
        if cnt > 0:
            for w in range(1, cnt+1):
                cnta[w] += cnt - w + 1
            cnt = 0
    else:
        cnt += 1
cnt = 0
for i in range(m+1):
    if i == m or b[i] == 0:
        if cnt > 0:
            for w in range(1, cnt+1):
                cntb[w] += cnt - w + 1
            cnt = 0
    else:
        cnt += 1

ans = 0
for x in range(1, n+1):
    if k % x == 0:
        y = k // x
        if y <= m:
            ans += cnta[x] * cntb[y]

print(ans)