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 math
n, m, k = [int(ele) for ele in input().split()]
a = [int(ele) for ele in input().split()]
b = [int(ele) for ele in input().split()]
lstA = []
lstB = []
prev = 0
for i in range(n):
    if a[i] == 1:
        if prev == 0:
            lstA.append(1)
        else:
            lstA[-1] += 1
        prev = 1
    else:
        prev = 0
prev = 0
for i in range(m):
    if b[i] == 1:
        if prev == 0:
            lstB.append(1)
        else:
            lstB[-1] += 1
        prev = 1
    else:
        prev = 0

factors = []
for i in range(1, int(math.sqrt(k)+1)):
    if i*i == k:
        factors.append([i, i])
    else:
        if i*(k//i) == k:
            factors.append([i, k//i])
            factors.append([k//i, i])

lst1 = []
lst2 = []
for i in range(n):
    lst1.append(0)
for i in range(m):
    lst2.append(0)

for ele in lstA:
    for i in range(1, ele+1):
        lst1[i-1] += ele-i+1

for ele in lstB:
    for i in range(1, ele+1):
        lst2[i-1] += ele-i+1

#print(lst1, lst2, factors)
count = 0
for factor in factors:
    if factor[0]-1 < n and factor[1]-1 < m:
        count += lst1[factor[0]-1]*lst2[factor[1]-1]
        #print(factor, count)

print(count)
