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 math import sqrt
from collections import Counter
def factor_pairs(k):
    pairs = []
    for i in range(1,int(sqrt(k)) + 1):
        if k % i == 0:
            pairs.append([i,k//i])
    length = len(pairs)
    if int(sqrt(k)) != sqrt(k):
        pairs.append(pairs[-1][::-1])
    for i in range(length-2,-1,-1):
        pairs.append(pairs[i][::-1])
    return pairs

def prog():
    n,m,k = map(int,input().split())
    a = "".join(input().split())
    b = "".join(input().split())
    pairs = factor_pairs(k)
    w_vals = Counter(map(len,a.split('0')))
    l_vals = Counter(map(len,b.split('0')))
    subrectangles = 0
    for width in w_vals:
        for length in l_vals:
            for x,y in pairs:
                if x > width:
                    break
                elif y <= length:
                    subrectangles += w_vals[width]*l_vals[length]*(width-x+1)*(length-y+1)
    print(subrectangles)
prog()
