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>


def process(a, b, k):
    a_factors = {}
    b_factors = {}
    n = len(a)
    m = len(b)
    for i in range(1, max(n, m)+1):
        if k % i==0 and 1 <= i <= n and 1 <= k//i <= m:
            a_factors[i] = 0
        if k % i==0 and 1 <= i <= m and 1 <= k//i <= n:
            b_factors[i]  = 0
    a_list = sorted(a_factors)
    b_list = sorted(b_factors)
    current = 0
    for i in range(n):
        if a[i]==1:
            current+=1
        else:
            for x in a_list:
                if current >= x:
                    a_factors[x]+=(current-x+1)
                else:
                    break
            current = 0
    for x in a_list:
        if current >= x:
            a_factors[x]+=(current-x+1)
        else:
            break
    current = 0
    for i in range(m):
        if b[i]==1:
            current+=1
        else:
            for x in b_list:
                if current >= x:
                    b_factors[x]+=(current-x+1)
                else:
                    break
            current = 0
    for x in b_list:
        if current >= x:
            b_factors[x]+=(current-x+1)
        else:
            break
    answer = 0
    for x in a_factors:
        if k//x in b_factors:
            answer+=(a_factors[x]*b_factors[k//x])
    return answer


                    
n, m, k = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]
print(process(a, b, k))
    
    
        
        
    