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())

a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

c = 0
aa = []
for e in a:
    if e == 1:
        c+=1
    elif c > 0:
        aa.append(c)
        c = 0
if c>0:
    aa.append(c)
#print(aa)

bb = []
c = 0
for e in b:
    if e == 1:
        c+=1
    elif c > 0:
        bb.append(c)
        c = 0
if c>0:
    bb.append(c)
#print(bb)

s = 0
for i in range(1, int(k ** 0.5) + 1):
    if k % i != 0:
        continue

   # print(i, k //i)
    k1, k2, l1, l2 = 0, 0 ,0 ,0
    for e in aa:
        if e >= i:
            k1 += e - i +1
        if e >= k // i:
            k2 += e - k // i + 1
    #print(k1, k2)
    for e in bb:
        if e >=i:
            l2 += e - i +1
        if e >= k // i:
            l1 += e - k // i + 1
    #print(l1, l2)
    #print("---")
    s += k1*l1
    if i != k // i:
        s+=k2*l2
print(s)
