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 collections import defaultdict
from math import factorial
from sys import stdin
#input = stdin.readline
def read_tuple(): return map(int,input().split())
def read_int(): return int(input())
def read_list(): return list(map(int,input().split()))
def factors(n):
    fact = []
    for i in range(1, int(n**0.5)+1):
        if n%i == 0:
            if n//i == i:
                fact.append(i)
            else:
                fact.append(i)
                fact.append(n//i)
    fact.sort()
    return fact

def comb(n,r):
    return factorial(n) // ( factorial(n-r)*factorial(r) )

n,m,k = read_tuple()
a = read_list()
b = read_list()
cnta, cntb = defaultdict(int), defaultdict(int)
cnta[0] = 0
cntb[0] = 0
cnt=0
for i in range(n):
    if a[i]==1: cnt+=1
    else:cnta[cnt]+=1; cnt=0
cnta[cnt]+=1
cnt = 0
for i in range(m):
    if b[i]==1: cnt+=1
    else: cntb[cnt]+=1; cnt=0
cntb[cnt]+=1

factor = factors(k)
ans = 0
for p1, cnt1 in cnta.items():
    for p2, cnt2 in cntb.items():
        if p1*p2 < k: continue
        for f in factor:
            f1, f2 = f, k//f
            if p1 >= f1 and p2 >= f2:
                ans += cnt1*cnt2*(p1-f1+1)*(p2-f2+1)
            
print(ans)