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, gettrace
from collections import Counter

if not gettrace():
    def input():
        return next(stdin)[:-1]


# def input():
#    return stdin.buffer.readline()

def main():
    n,m,k = map(int, input().split())
    aa = input().split()
    bb = input().split()
    if m < n:
        aa, bb = bb, aa
        n, m = m, n
    asegs = sums(aa, n)
    bsegs = sums(bb, m)

    res = 0
    for i in range(1, min(n,k)+1):
        if k%i == 0 and k//i <= m:
            res +=  asegs[i] * bsegs[k//i]
    print(res)

def sums(aa, n):
    acounts = [0] * (n + 1)
    ocount = 0
    for a in aa:
        if a == '1':
            ocount += 1
        else:
            acounts[ocount] += 1
            ocount = 0
    acounts[ocount] += 1
    amsum = 0
    for i in range(1,n+1):
        amsum += acounts[i] * i
    asum = [0] * (n + 2)
    for i in range(n, 0, -1):
        asum[i] = asum[i + 1] + acounts[i]
    segs = [0, amsum]
    for i in range(2, n + 1):
        segs.append(segs[-1] - asum[i - 1])

    return segs

if __name__ == "__main__":
    main()


