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>
def getContiguous(arr): #returns list of lengths of contiguous 1s
    n=len(arr)
    cnt=0
    res=[]
    for i in range(n):
        if arr[i]==1:
            cnt+=1
        else:
            if cnt>0:
                res.append(cnt)
            cnt=0
    if cnt>0:
        res.append(cnt)
    return res
            


n,m,k=[int(x) for x in input().split()]
a=[int(x) for x in input().split()]
b=[int(x) for x in input().split()]

aOnes=getContiguous(a)
bOnes=getContiguous(b)

aCounts=[0 for __ in range(n+1)] #aCounts[i] is the number of occurrences of contiguous '1's with size i
bCounts=[0 for __ in range(m+1)]

for c in aOnes:
    aCounts[c]+=1
for c in bOnes:
    bCounts[c]+=1

add=0
add2=0
for i in range(n,-1,-1):
    add+=aCounts[i]
    add2+=add
    aCounts[i]=0
    aCounts[i]+=add2
    
add=0
add2=0
rollingTotal=0
for i in range(m,-1,-1):
    add+=bCounts[i]
    add2+=add
    bCounts[i]=0
    bCounts[i]+=add2

validRectangleDimensions=[]
for i in range(1,int(k**0.5)+1):
    if k%i==0:
        validRectangleDimensions.append([i,k//i])
        if i!=k//i: #append the transpose
            validRectangleDimensions.append([k//i,i])

ans=0
for dimx,dimy in validRectangleDimensions:
    if dimx<=n and dimy<=m:
#        print(dimx,dimy,aCounts[dimx],bCounts[dimy])
        ans+=aCounts[dimx]*bCounts[dimy]
#print(aCounts)
#print(bCounts)
print(ans)