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>
from math import sqrt

N, M, K = map(int,raw_input().split())

facts = set()
for k in range(1, int(sqrt(K))+1) :
  if K % k == 0 : 
    facts.add(k)
    facts.add(K//k)
  
a = map(int,raw_input().split())
b = map(int,raw_input().split())

pa, pb = [0], [0]
endA, endB = [], []
for n in range(N) : 
  pa.append((pa[-1]+a[n]) * a[n])
  if pa[-1] == 0 : endA.append(pa[-2])
for m in range(M) : 
  pb.append((pb[-1]+b[m]) * b[m])
  if pb[-1] == 0 : endB.append(pb[-2])

endA.append(pa[-1])
endB.append(pb[-1])

#print endA
#print endB
#print facts

ans = 0
for f in facts :
  cntA, cntB = 0, 0
  for i in range(len(endA)) : cntA += max(0, endA[i]-f+1)
  for i in range(len(endB)) : cntB += max(0, endB[i]-K//f+1)
  
  #print "cnt:", cntA, cntB
  ans += cntA*cntB

print ans