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()))
 
a1=[]
b1=[]
x=[]
c=0
out=0  
f=0
for i in range(n):
    if(a[i]==1):
        if(f==0):
            c=1
            f=1
        else:
            c+=1
        
 
    else:
        if(f==1):
            f=0
            
            a1.append(c)
            c=0
        else:
            continue
if(f==1):
    a1.append(c)
    c=0
f=0
c=0
for i in range(m):
    if(b[i]==1):
        if(f==0):
            c=1
            f=1
        else:
            c+=1
        
 
    else:
        if(f==1):
            f=0
            
            b1.append(c)
            c=0
        else:
            continue
if(f==1):
    b1.append(c)
    c=0
for i in range(1,int(k**(0.5))+1):
    if(k%i==0):
        if(i!=k//i):
            x.append(i)
            x.append(k//i)
        else:
            x.append(i)
for p in x:
    q=k//p
    y=0
    z=0
    for i in a1:
        if(i>=p):
            y+=i-p+1
    for i in b1:
        if(i>=q):
            z+=i-q+1
    out+=y*z
print(int(out))