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
from collections import defaultdict

def search(a, t):
    l = 0
    r = len(a)-1
    ans = 0
    
    while (r-l)>=0:
        mid = (l+r)//2
        if a[mid] < t:
            l = mid+1
        if a[mid] >= t:
            r = mid-1
            ans = mid
            
    return ans

def getFactors(n): 
    factors = []
    i = 1
    while i <= math.sqrt(n): 
        if (n % i == 0) : 
            if (n // i == i) : 
                factors.append(i)
            else : 
                factors.append(i)
                factors.append(n//i)
        i = i + 1
    return factors

n, m, k = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
d = defaultdict(int)
factors = getFactors(k)
a_s = []
b_s = []
ct = 0

for i in range(n):
    if a[i]:
        ct += 1
    else:
        if ct:
            a_s.append(ct)
            ct = 0
            
if ct:
    a_s.append(ct)
    
ct = 0
for i in range(m):
    if b[i]:
        ct += 1
    else:
        if ct:
            b_s.append(ct)
            ct = 0
            
if ct:
    b_s.append(ct)
    
a_s.sort()
b_s.sort()
ans = 0

for i in factors:
    d[i] = sum([max(0, 1+b_s[j]-i) for j in range(len(b_s))])
    
for i in factors:
    for j in a_s:
        if j >= i:
            ans += (1+j-i)*d[k//i]
            
print(ans)