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>
l1,l2,req = (int(i) for i in input().split(' '))
lia = [int(i) for i in input().split(' ')]
lib = [int(i) for i in input().split(' ')]

ca = {}
cb = {}

tmp = 0
for i in lia:
    if i == 1:
        tmp += 1
    else:
        if tmp:
            ca[tmp] = ca.get(tmp,0)+1
        tmp = 0

if tmp:
    ca[tmp] = ca.get(tmp,0)+1


tmp = 0
for i in lib:
    if i == 1:
        tmp += 1
    else:
        if tmp:
            cb[tmp] = cb.get(tmp,0)+1
        tmp = 0

if tmp:
    cb[tmp] = cb.get(tmp,0)+1

ans = 0


for keyi,vali in ca.items():
    for keyj,valj in cb.items():
        if keyi*keyj >= req:
            for t in range(1,1+keyi):
                if req%t == 0 and req//t <= keyj:
                    ans += vali*valj*(keyi-t+1)*(keyj-req//t+1)

# print(ca)
# print(cb)
print(ans)
# prea = {}
# preb = {}
# tmp = 0
# for k,v in sorted(ca,reverse=True):
#     tmp += ca[k]
#     prea[k] = tmp 
# tmp = 0
# for k,v in sorted(cb,reverse=True):
#     tmp += cb[k]
#     preb[k] = tmp 

# for i in ca:
#     for j in cb:
#         if i*j >= req:
#             for t in range(1,1+i):
#                 if req%t == 0 and req//t <= j:
#                     ans += (i-t+1)*(j-req//t+1)
# print(ans)