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>
from sys import stdin
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
from collections import deque
from bisect import bisect_left
n,m,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
da={}
s=set()
f=0
x=0
for i in range(n):
	if a[i]==1:
		if f==0:
			x=1
			f=1
		elif f==1:
			x+=1
	else:
		if f==1:
			if x in da:
				da[x]+=1
			else:
				da[x]=1
			s.add(x)
			x=0
			f=0
if x>0:
	if x in da:
		da[x]+=1
	else:
		da[x]=1
	s.add(x)
sa=sorted(s)
db={}
s=set()
f=0
x=0
for i in range(m):
	if b[i]==1:
		if f==0:
			x=1
			f=1
		elif f==1:
			x+=1
	else:
		if f==1:
			if x in db:
				db[x]+=1
			else:
				db[x]=1
			s.add(x)
			x=0
			f=0
if x>0:
	if x in db:
		db[x]+=1
	else:
		db[x]=1
	s.add(x)
sb=sorted(s)
l=[]
i=1
while i*i<=k:
	if k%i==0:
		l.append([i,k//i])
	i+=1
ans=0
# print(l,sa,sb)
for i in l:
	x=bisect_left(sa,i[0])
	y=bisect_left(sb,i[1])
	count1=0
	count2=0
	for j in range(x,len(sa)):
		count1+=da[sa[j]]*(sa[j]-i[0]+1)
	for j in range(y,len(sb)):
		count2+=db[sb[j]]*(sb[j]-i[1]+1)
	ans+=(count1*count2)
	# print(x,y)
	if i[0]!=i[1]:
		x=bisect_left(sa,i[1])
		y=bisect_left(sb,i[0])
		count1=0
		count2=0
		for j in range(x,len(sa)):
			count1+=da[sa[j]]*(sa[j]-i[1]+1)
		for j in range(y,len(sb)):
			count2+=db[sb[j]]*(sb[j]-i[0]+1)
		ans+=(count1*count2)
print(ans)