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
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

def main():
    def ser(aa):
        pa=aa[0]
        w=1
        res=defaultdict(int)
        for a in aa[1:]:
            if pa==a:
                w+=1
            else:
                if pa==1:res[w]+=1
                w=1
            pa=a
        if pa == 1: res[w] += 1
        return res

    def divs(k):
        res=[]
        for i in range(1,k+1):
            if i**2>k:break
            if k%i==0:
                res.append(i)
                res.append(k//i)
        if res[-1]**2==k:res.pop()
        return res

    def cntl(cnta,la):
        res=0
        for w,c in cnta.items():
            if w-la+1>0:res+=(w-la+1)*c
        return res

    n,m,k=MI()
    dd=divs(k)
    aa=LI()
    bb=LI()
    cnta=ser(aa)
    cntb=ser(bb)
    ans=0
    for la in dd:
        lb=k//la
        ans+=cntl(cnta,la)*cntl(cntb,lb)

    print(ans)

main()