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()))
nfact=0
fact=[]
i=1
while i*i<=k:
    if k%i==0:
        nfact+=1
        fact=fact+[i]
        if i*i<k:
            nfact+=1
            fact=fact+[k//i]
    i=i+1
fact.sort()
facta=[0]*nfact
factb=[0]*nfact
cur=0
for i in range(n):
    if a[i]==1:
        cur+=1
    else:
        if cur>0:
            j=0
            while j<nfact and cur>=fact[j]:
                if cur>=fact[j]:
                    facta[j]=facta[j]+cur-fact[j]+1
                j=j+1
            cur=0
if cur>0:
    j=0
    while j<nfact and cur>=fact[j]:
        if cur>=fact[j]:
            facta[j]=facta[j]+cur-fact[j]+1
        j=j+1
cur=0

for i in range(m):
    if b[i]==1:
        cur+=1
    else:
        if cur>0:
            j=0
            while j<nfact and cur>=fact[j]:
                if cur>=fact[j]:
                    factb[j]=factb[j]+cur-fact[j]+1
                j=j+1
                
            cur=0
if cur>0:
    j=0
    while j<nfact and cur>=fact[j]:
        if cur>=fact[j]:
            factb[j]=factb[j]+cur-fact[j]+1
        j=j+1
sol=0
for i in range(nfact):
    sol=sol+facta[i]*factb[-i-1]
print(sol)
