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 math
n, m, k = [int(x) for x in input().split()]

a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

delitele = []

for i in range(int(math.sqrt(k))):
    if k%(i+1) == 0:
        delitele.append([i+1, k//(i+1)])

acka = []
doteraz = 0
suvisle = True
for i in range(n):
    if a[i] == 1 and suvisle:
        doteraz += 1
    if a[i] == 0 and suvisle:
        acka.append(doteraz)
        suvisle = False
    if a[i] == 1 and not suvisle:
        doteraz = 1
        suvisle = True
    if a[i] == 1 and i == n-1:
        acka.append(doteraz)

bcka = []
doteraz = 0
suvisle = True
for i in range(m):
    if b[i] == 1 and suvisle:
        doteraz += 1
    if b[i] == 0 and suvisle:
        bcka.append(doteraz)
        suvisle = False
    if b[i] == 1 and not suvisle:
        doteraz = 1
        suvisle = True
    if b[i] == 1 and i == m-1:
        bcka.append(doteraz)


moznosti = 0
for i in range(len(delitele)):
    prvy = delitele[i][0]
    druhy = delitele[i][1]
    moznostiA = 0
    moznostiB = 0
    for j in range(len(acka)):
        if acka[j] >= prvy:
            moznostiA += acka[j] - prvy + 1
    for j in range(len(bcka)):
        if bcka[j] >= druhy:
            moznostiB += bcka[j] - druhy + 1
    moznosti = moznosti + moznostiA * moznostiB

    if prvy != druhy:
        moznostiA = 0
        moznostiB = 0
        for j in range(len(acka)):
            if acka[j] >= druhy:
                moznostiA += acka[j] - druhy + 1
        for j in range(len(bcka)):
            if bcka[j] >= prvy:
                moznostiB += bcka[j] - prvy + 1
        moznosti = moznosti + moznostiA * moznostiB

print(moznosti)
