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 math
from sys import stdin
I=stdin.readline
for _ in range(1):
    n,m,k=map(int,I().split())
    ar=list(map(int,I().split()))
    br=list(map(int,I().split()))
    prv=0
    la=[]
    lb=[]
    for i in range(n):
        if ar[i]==1:
            prv+=1
        elif prv!=0 and ar[i]==0:
            la.append(prv)
            prv=0
    if prv!=0:
        la.append(prv)
        prv=0
    for i in range(m):
        if br[i]==1:
            prv+=1
        elif prv!=0 and br[i]==0:
            lb.append(prv)
            prv=0
    if prv!=0:
        lb.append(prv)
        prv=0
    lena=len(la)
    lenb=len(lb)

    div =[i for i in range(1,int(k**0.5)+1) if k%i==0]# divisors(k)
    div+=[k//i for i in div if i!=k//i]
    ldiv=len(div)
    cnt=0
    cnt1=0
    cnt2=0
    for ij in range(ldiv):
        for i in range(lena):
            if div[ij]>la[i]:
                fl=1
                continue
            var=la[i]+1-div[ij]
            if var<0:
                var=0
            cnt1+=var
           # print(var,cnt1)
        for j in range(lenb):
            if k//div[ij]>lb[j] :
                continue
            var=lb[j]+1-(k//div[ij])
            if var<0:
                var=0
            cnt2+=var
    
        cnt+=cnt1*cnt2
        cnt1=0
        cnt2=0
    print(cnt)
                
        
            
        
        
        
    
