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 collections import Counter
import atexit
import io
import sys
_INPUT_LINES = sys.stdin.read().splitlines()
raw_input = iter(_INPUT_LINES).next
_OUTPUT_BUFFER = io.BytesIO()
sys.stdout = _OUTPUT_BUFFER
 
@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
    
def takla():
    n,m,k=map(int,raw_input().split())
    a=[int(o) for o in raw_input().split()]
    b=[int(o) for o in raw_input().split()]
    a.append(0)
    b.append(0)
    for i in range(n):
        a[i]=(a[i-1]+1 if a[i]==1 else 0)
    d=dict(Counter(a))
    # print(d)
    dk=sorted(list(d.keys()))
    dk=dk[::-1]
    dk.pop()
    for i in range(1,len(dk)):
        d[dk[i]]+=d[dk[i-1]]
    # print(d)
    ans=0
    for i in range(m):
        b[i]=(b[i-1]+1 if b[i]==1 else 0)
    d1=dict(Counter(b))
    # print(d)
    dk=sorted(list(d1.keys()))
    dk=dk[::-1]
    dk.pop()
    for i in range(1,len(dk)):
        d1[dk[i]]+=d1[dk[i-1]]
    for j in d1.keys():
        if j!=0:
            if j<=k and k%j==0:
                k1=k//j
                if k1 in d:
                    # print(k1,j)
                    ans+=(d[k1]*d1[j])
    # print(d)
    # print(d1)
    print(ans)
    
      
    
if __name__ == "__main__":
	takla()