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 sys
input = sys.stdin.readline
n,m,k = map(int,input().split())
a = tuple(map(int,input().split()))
b = tuple(map(int,input().split()))
pairs = []
for i in range(1,int(k**0.5)+1):
    if k%i==0:
        pairs.append((i,k//i))
sa = 0
sb = 0
pa = [0]
pb = [0]
for i in range(n):
    sa+=a[i]
    pa.append(sa)
for i in range(m):
    sb+=b[i]
    pb.append(sb)
ans = 0
for fa,fb in pairs:
    c1 = 0
    c2 = 0
    for i in range(n-fa+1):
        if pa[i+fa]-pa[i]==fa:
            c1+=1
    for i in range(m-fb+1):
        if pb[i+fb]-pb[i]==fb:
            c2+=1
    ans+=c1*c2
    c1,c2=0,0
    if fa==fb:
        continue
    for i in range(n-fb+1):
        if pa[i+fb]-pa[i]==fb:
            c1+=1
    for i in range(m-fa+1):
        if pb[i+fa]-pb[i]==fa:
            c2+=1
    ans+=c1*c2
print(ans)
