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 
def ff(a, r):
    fa = fb = [-1]*40002
    la = lb = []
    l = 0
    i = 0
   
    for i in range(r):
        if a[i] == 1:
            l = l+1
        elif l > 0:
            if fa[l] == -1:
                fa[l] = len(la)
                la.append([l,1])
            else:
                la[fa[l]][1] +=1
            l = 0
    if l > 0:
        if fa[l] == -1:
            fa[l] = len(la)
            la.append([l,1])
        else:
            la[fa[l]][1] +=1
            l = 0
    return la
r, c, k = list(map(int, input().split()))
a = list(map(int, input().split()))
b = list(map(int, input().split()))

la = ff(a,r)
lb = ff(b,c)
d = []
lim = int(math.sqrt(k))
for i in range(lim):
    if k % (i+1) == 0:
        d.append([i+1,int(k/(i+1))])
ans = 0
for i in d:
    for j in la:
        for k in lb:
            #print(i,j,k)
            if i[0] <= j[0] and i[1] <= k[0]:
                tmp = (-i[0]+j[0]+1)*(-i[1]+k[0]+1)
                ans = ans + tmp*j[1]*k[1]
            if i[0]!=i[1]:
                if i[0] <= k[0] and i[1] <= j[0]:
                    t = (-i[0]+k[0]+1)*(-i[1]+j[0]+1)
                    ans = ans + t*j[1]*k[1]
print(ans)