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>
#import numpy as np
#line1="3 5 4".split(" ")
line1=input().split(" ")

for i in range(3):
	line1[i]=int(line1[i])
n,m,k=line1
a=dict()
b=dict()
def output(inp,arr,n,k):
	c=0
	for i in range(n): 
		if inp[i]=="1":
			c+=1
		else:
			d=min(c+1,k+1)
			for j in range(1,d):
				if j not in arr:
					arr[j]=c+1-j
				else:
					arr[j]+=c+1-j
			c=0
	d=min(c+1,k+1)
	for j in range(1,d):
		if j not in arr:
			arr[j]=c+1-j
		else:
			arr[j]+=c+1-j
	return arr
a=output(input().split(" "),a,n,k)
b=output(input().split(" "),b,m,k)

#line3=input().split(" ")
#line3="1 1 1".split(" ")
#print(a,b)
output=0
for i in range(1,n+1):
	if k%i==0:
		if i in a and k//i in b:
		#print(1)
			output+=a[i]*b[k//i]
print("%d"%(output))




