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 sys
input = sys.stdin.readline
from collections import *

n, m, k = map(int, input().split())
a = list(map(int, input().split()))+[0]
b = list(map(int, input().split()))+[0]
cnt1 = [0]*(n+1)
now = 0

for i in range(n+1):
    if a[i]==0:
        for j in range(1, now+1):
            cnt1[j] += now-j+1
        
        now = 0
    else:
        now += 1

cnt2 = [0]*(m+1)
now = 0

for i in range(m+1):
    if b[i]==0:
        for j in range(1, now+1):
            cnt2[j] += now-j+1
        
        now = 0
    else:
        now += 1

ans = 0

for i in range(1, int(k**0.5)+1):
    if k%i==0:
        if i<=n and k//i<=m:
            ans += cnt1[i]*cnt2[k//i]
        
        if i!=k//i:
            if k//i<=n and i<=m:
                ans += cnt1[k//i]*cnt2[i]

print(ans)