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()))
fact=[]
for i in range(1,int(k**0.5)+1):
	if k%i==0:
		fact.append(i)
		if i!=(k//i):
			fact.append(k//i)
arr=[0]*(len(a)+1)
brr=[0]*(len(b)+1)
for i in range(n):
	arr[i+1]=arr[i]+a[i]
for i in range(m):
	brr[i+1]=brr[i]+b[i]
# print(arr)
# print(brr)
ans=0
for i in range(1,n+1):
	if k%i==0 and k//i<=m:
		aa=0
		bb=0
		x=i 
		y=k//i 
		for ii in range(x,n+1):
			if arr[ii]-arr[ii-x]==x:
				aa+=1
		for jj in range(y,m+1):
			if brr[jj]-brr[jj-y]==y:
				bb+=1
		ans+=(aa*bb)
print(ans)