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>
from sys import stdin
from math import sqrt

n, m, k = list(map(int, stdin.readline().split(" ")))

A = list(map(int, stdin.readline().split(" ")))
B = list(map(int, stdin.readline().split(" ")))

A_dic = []
cur_length = 0
for i in range(n):
    if A[i] == 1:
        cur_length += 1
    else:
        if cur_length != 0:
            A_dic.append(cur_length)
        cur_length = 0
if cur_length != 0:
    A_dic.append(cur_length)
A.clear()

B_dic = []
cur_length = 0
for i in range(m):
    if B[i] == 1:
        cur_length += 1
    else:
        if cur_length != 0:
            B_dic.append(cur_length)
        cur_length = 0
if cur_length != 0:
    B_dic.append(cur_length)

B.clear()

sum = 0

if len(A_dic) == 0 or len(B_dic) == 0:
    print(0)
    exit()

A_dic.sort(reverse=True)
B_dic.sort(reverse=True)
max_A = A_dic[0]
max_B = B_dic[0]
if max_A * max_B < k:
    print(sum)
    exit()

else:
    for i in range(1, int(sqrt(k)) + 1):
        if k % i == 0:
            factor1 = i
            factor2 = k / i
            if factor1 <= max_A and factor2 <= max_B and factor1 != factor2:
                choose_A = 0
                choose_B = 0

                for item in A_dic:
                    if item < factor1:
                        break
                    else:
                        choose_A += (item - factor1 + 1)

                for item in B_dic:
                    if item < factor2:
                        break
                    else:
                        choose_B += (item - factor2 + 1)

                sum += (choose_A * choose_B)

            if factor2 <= max_A and factor1 <= max_B:
                choose_A = 0
                choose_B = 0

                for item in A_dic:
                    if item < factor2:
                        break
                    else:
                        choose_A += (item - factor2 + 1)

                for item in B_dic:
                    if item < factor1:
                        break
                    else:
                        choose_B += (item - factor1 + 1)

                sum += (choose_A * choose_B)

print(int(sum))
exit()