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
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__
import math
from functools import reduce

def factors(n):    
    return set(reduce(list.__add__, 
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))

def countit(lst,lenr):
    n=len(lst)
    counter=0
    if lenr>n:
        return 0
    else:
        subcounter=0
        for i in range(n):
            if lst[i]==1:
                subcounter+=1 
            else:
                if subcounter>=lenr:
                    counter+=(subcounter-lenr+1)
                subcounter=0
            if i==n-1:
                if subcounter>=lenr:
                    counter+=(subcounter-lenr+1)
    return counter
#print(countit([1,1,1,1],3))
        
if __name__ == '__main__':
    n,m,k = list(map(int,input().split()))
    a1=list(map(int,input().split()))
    a2=list(map(int,input().split()))
##    res=[]
##    for i in range(n):
##        res.append(list(map(lambda x:x*a1[i],a2)))
##    print(res)
    factk=list(factors(k))
    factk.sort()
    recdimen=[]
    for ele in factk:
        if ele<=(k**0.5):
            recdimen.append([ele,k//ele])
        else:
            break
    res=0
    #print(recdimen)
    for dima,dimb in recdimen:
        ta1,ta2=countit(a1,dima),countit(a2,dimb)
        tb1,tb2=countit(a2,dima),countit(a1,dimb)

        if dima==dimb:
            res+=(ta1*ta2)
        else:
            res+=(ta1*ta2+tb1*tb2)
    print(res)
