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>
n,m,k = map(int,input().split())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
length = {}
length2 = {}
t = 0
for i in range(n):
  if a[i] == 1:
    t += 1
  if (a[i] == 0) and (t>0):
    if length.get(t) == None:
      length[t] = 1
    else:
      length[t] += 1
    t = 0
if t>0:
  if length.get(t) == None:
    length[t] = 1
  else:
    length[t] += 1
p = {}
t = 0
for i in range(m):
  if b[i] == 1:
    t += 1
  if (b[i] == 0) and (t>0):
    if length2.get(t) == None:
      length2[t] = 1
    else:
      length2[t] += 1
    t = 0
if t>0:
  if length2.get(t) == None:
    length2[t] = 1
  else:
    length2[t] += 1
for i in length.keys():
  for j in length2.keys():
    if i>=j:
      h = (j,i)
    else:
      h = (i,j)
    if p.get(h) == None:
      p[h] = length[i]*length2[j]
    else:
      p[h] += length[i]*length2[j]
divisors = []
g = int(k**0.5)
for d in range(1,g+1):
  if k%d == 0:
    w = k//d
    divisors.append([d,w])
    if w != d:
      divisors.append([w,d])
divisors.sort()
s = 0
for r in p.keys():
  if r[0]*r[1]<k:
    continue
  for f in divisors:
    if f[0]>r[0]:
      break
    if f[1]>r[1]:
      continue
    s += (r[1]-f[1]+1)*(r[0]-f[0]+1)*p[r]
print(s)
      
