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>
# maa chudaaye duniya
def getdivs(n):
    i = 1
    a = []
    while i <= int(n**0.5):
        if n%i == 0:
            if n//i == i:
                a.append(i)
            else:
                a += [i, n//i]
        i += 1
    return sorted(a)

def getConsecutive(arr):
    arr = [0] + arr + [0]
    sz = 1
    maps = {}
    maps[1] = arr.count(1)
    # print(arr)
    # print([i for i in range(len(arr))])
    for i in range(1, len(arr)):
        if arr[i] == arr[i-1] and arr[i] == 1:
            sz += 1
            # print(i, i-1, sz)
        else:
            cnt = 1
            while sz > 1 and sz > 1:
                if sz in maps:
                    maps[sz] += cnt
                else:
                    maps[sz] = cnt
                cnt += 1
                sz -= 1 
            sz = 1
    return (maps)

# getConsecutive([1,1,1,1,1,0,1,1,1])
n, m, k = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
divis = getdivs(k)
map1 = getConsecutive(a)
map2 = getConsecutive(b)
# print(divis)
# print(map1)
# print(map2)
su = 0
for i in divis:
    cur = i
    second = k // cur
    # print(cur, second)
    if cur in map1 and second in map2:
        su += map1[cur] * map2[second]
print(su)