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>
''' Count Subrectangles
'''

from math import sqrt

def computesizes(Aarr, Barr, N, M, dims):
    Awidths, Bwidths = [], []
    acount, bcount = 0, 0
    axiscounts = [[0, 0] for dim in dims]
    for n, A in enumerate(Aarr):
        if A == 1:
            acount += 1
            if n == N - 1:
                Awidths.append(acount)
        elif acount > 0 and A == 0:
            Awidths.append(acount)
            acount = 0

    for m, B in enumerate(Barr):
        if B == 1:
            bcount += 1
            if m == M - 1:
                Bwidths.append(bcount)
        elif bcount > 0 and B == 0:
            Bwidths.append(bcount)
            bcount = 0

    for A in Awidths:
        for n, dim in enumerate(dims):
            axiscounts[n][1] += max(A - dim[1] + 1, 0)

    for B in Bwidths:
        for n, dim in enumerate(dims):
            axiscounts[n][0] += max(B - dim[0] + 1, 0)
    
    blocks = sum(count[0]*count[1] for count in axiscounts)
    return blocks

def computedims(K):
    bound = int(sqrt(K))
    dims = []
    for f in range(1, bound + 1):
        if K % f == 0:
            dims.append((f, K//f))
            if f**2 != K:
                dims.append((K//f, f))
    
    return dims

''' routine '''

N, M, K = list(map(int, input().split()))
dims = computedims(K)
# print(dims)

Aarr = list(map(int, input().split()))
Barr = list(map(int, input().split()))

blockcount = computesizes(Aarr, Barr, N, M, dims)

print(blockcount)