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())
l1=list(map(int,input().split()))
l2=list(map(int,input().split()))
factors=[]
for i in range(1,int(k**0.5)+1):
	if k%i==0:
		factors.append((i,k//i))
		if i!=k//i:
			factors.append((k//i,i))
# print (factors)
g1,g2=[],[]
count=l1[0]
for i in range(1,n):
	if l1[i]==0 and l1[i-1]==1:
		g1.append(count)
		count=0
	elif l1[i]==1:
		count+=1
if count!=0:
	g1.append(count)
count=l2[0]
for i in range(1,m):
	if l2[i]==0 and l2[i-1]==1:
		g2.append(count)
		count=0
	elif l2[i]==1:
		count+=1
if count!=0:
	g2.append(count)
# print (g1,g2)
ans=0
for i in factors:
	count1=[]
	count2=[]
	for j in g1:
		if j>=i[0]:
			count1.append((j-i[0]+1))
	for j in g2:
		if j>=i[1]:
			count2.append((j-i[1]+1))
	for j in count1:
		for k in count2:
			ans+=j*k
print (ans)