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 nums(arr):
    con=[]
    n=len(arr)
    l=-1
    for i in xrange(n):
        if arr[i]==1:
            if l==-1:
                l=i
        else:
            if l!=-1:
                con.append(i-l)
                l=-1
        if i==n-1 and arr[i]==1:
            con.append(n-l)
    arr=[0]*(n+1)
    # print con
    for i in xrange(len(con)):
        j=1
        while j<=con[i]:
            # print con[i], j, con[i]-j+1
            if con[i]-j+1>0:
                arr[j]+=con[i]-j+1
            j+=1
    return arr

n,m,k=map(int, raw_input().split())
N=map(int, raw_input().split())
M=map(int, raw_input().split())


numsN=nums(N)
numsM=nums(M)

# print numsN
# print numsM

res=0
for i in xrange(1, n+1):
    # print k, i, k/i
    if k%i==0 and k/i<=m:
        res+=numsN[i]*numsM[k/i]
print res

