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().split())
list1 = list(map(int,input().split()))
list2 = list(map(int,input().split()))

conce_1 = []
conce_2 = []
i=0
while i<(n):
    if list1[i]==1:
        count=0
        while i<len(list1) and list1[i]==1:
            i+=1
            count+=1
        conce_1.append(count)
    else:
        i+=1
i=0
while i<m:
    if list2[i]==1:
        count=0
        while i<len(list2) and list2[i]==1:
            i+=1
            count+=1
        conce_2.append(count)
    else:
        i+=1
if len(conce_1)==0:
    print(0)
else:
    p = max(conce_1)
    ans=0
    for i in range(1,p+1):
        t = k/i
        if t==int(t):
            s1=0
            for j in range(len(conce_1)):
                if conce_1[j]-(i-1) >0:
                    s1+=(conce_1[j]-(i-1))
            s2=0
            for j in range(len(conce_2)):
                if conce_2[j]-(t-1)>0:
                    s2+=conce_2[j]-(t-1)

            ans+=(s1*s2)
    print(int(ans))






