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 math  
  
# Method to print the divisors 
def printDivisors(n,l) : 
    list = []  
      
    # List to store half of the divisors 
    for i in range(1, int(math.sqrt(n) + 1)) : 
          
        if (n % i == 0) : 
              
            # Check if divisors are equal 
            if (n / i == i) : 
                l.append(i)
            else : 
                # Otherwise print both 
                l.append(i) 
                list.append(int(n / i)) 
                  
    # The list will be printed in reverse     
    for i in list[::-1] : 
        l.append(i)

n,m,k=map(int,input().split())
l1=list(map(int,input().split()))
l2=list(map(int,input().split()))
seq1=[]
seq2=[]
l=0
for i in range(n):
	if(l1[i]==1):
		l+=1
		if(i==n-1):
			seq1.append(l)

	else:
		if(l>0):
			seq1.append(l)
			l=0
l=0
for i in range(m):
	if(l2[i]==1):
		l+=1
		if(i==m-1):
			seq2.append(l)
	else:
		if(l>0):
			seq2.append(l)
			l=0
list_of_div=[]
printDivisors(k,list_of_div)
#print(list_of_div)
#print(seq1)
#print(seq2)
summ=0
for i in range(len(list_of_div)):
	a=0
	b=0
	for j in range(len(seq1)):
		if(seq1[j]>=list_of_div[i]):
			a+=seq1[j]-list_of_div[i]+1
	for j in range(len(seq2)):
		if(seq2[j]>=(k//list_of_div[i])):
			b+=seq2[j]-(k//list_of_div[i])+1
	summ+=(a*b)
print(summ)












