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, m, k = map(int, input().strip().split())

arr1 = list(map(int, input().strip().split()))
arr2 = list(map(int, input().strip().split()))



rects = []
dicti = {}

conts = []
j = 0
for i in arr2:
    if i == 1:
        j += 1
    else:
        conts.append(j)
        j = 0
if j > 0:
    conts.append(j)
# print(conts)
for i in range(1, len(arr1)+1):
    if k%i == 0:
        sumi = 0
        for j in conts:
            sumi += max(0, j-k//i+1)
        rects.append([i, sumi])
# print(rects)
for i in range(1, len(rects)):
    rects[i][1] += rects[i-1][1]

for i in rects:
    dicti[i[0]] = i[1]

j = 1
dp = [0 for i in range(len(arr1)+1)]
# print(dicti)
for i in range(1, len(arr1)+1):
    if i in dicti:
        j = i
    dp[i] = dp[i-1] + dicti[j]

ans = 0
# print(dp)

cont = 0
for i in range(len(arr1)):
    if arr1[i] == 1:
        cont += 1
    else:
        ans += dp[cont]
        cont = 0

if cont > 0:
    ans += dp[cont]

print(ans)








