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
from sys import stdin
import math

#your code goes here
def solve():
    n,m,k = list(map(int,input().split()))
    a = list(map(int,input().split()))
    b = list(map(int,input().split()))
    l = [0] * (n + 2)
    r = [0] * (m + 2)
    i = 0
    while i < n :
        if a[i] == 1 :
            j = i
            while j < n and a[j] == 1 :
                j += 1
            for t in range(1,j - i + 1) :
                l[t] += j - i - t + 1
            i = j
        else :
            i += 1

    i = 0
    while i < m:
        if b[i] == 1 :
            j = i
            while j < m and b[j] == 1 :
                j += 1
            for t in range(1, j - i + 1):
                r[t] += j - i - t + 1
            i = j
        else :
            i += 1
    ans = 0
    sqrtK = int(math.sqrt(k))
    for x in range(1,min(n + 1,sqrtK + 1)) :
        if k % x == 0 :
            y = int(k / x)
            if y <= m :
                ans += l[x] * r[y]
            if x != y and x <= m and y <= n:
                ans += l[y] * r[x]
    print(ans)
def main():
   # sys.stdin = open("test.inp", "r")
    solve()

if __name__ == "__main__":
    main()
