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 cal_sum(lena,lenb, suma, sumb):
    if lena >= len(suma) or lenb >= len(sumb):
        return 0
    return suma[lena]*sumb[lenb]

def build_sum_arr(arr, sum_arr):
    i = 0
    j = 0
    while i < len(arr):
        if arr[i] == 1:
            j = i
            while i < len(arr) and arr[i] == 1:
                i = i + 1
            ln = i-j
            count = 1
            for ki in range(ln,0,-1):
                # print(ki, i, j, arr)
                sum_arr[ki] = sum_arr[ki] + count
                count = count + 1
        i = i + 1
    return sum_arr

n, m, k = [int(i) for i in input().split(' ')]
a = [int(i) for i in input().split(' ')]
b = [int(i) for i in input().split(' ')]

suma = [0 for i in range(0,len(a) + 1)]
sumb = [0 for i in range(0,len(b) + 1)]

suma = build_sum_arr(a,suma)
sumb = build_sum_arr(b,sumb)

i = 1
sums = 0
while i*i <= k:
    if k % i == 0:
        sums = sums + cal_sum(i,int(k/i),suma,sumb)
        if i*i != k:
            sums = sums + cal_sum(int(k/i),i,suma,sumb)
    i = i + 1
print(sums)
