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>
'''
//////////////////////////////////////////////////////////////////////////////////////////////
//                                                                                          //
//                                   Coded by Ashish                                        //
//                                                                                          //
/////////////////////////////////////////////////////////////////////////////////////////////
'''
import math
def printDivisors(n) : 
    l=[]
    i = 1
    while i <= math.sqrt(n):
        if (n % i == 0) : 
            if (n / i == i) : 
                l.append(i) 
            else : 
                l.append(i)
        i = i + 1
    l.sort()    
    return l    
#q=int(input())
q=1
for _ in range(q):
    n,m,k=map(int,input().split())
    a=list(map(int,input().split()))
    b=list(map(int,input().split()))
    l=printDivisors(k)
    ans=0
    for j in range(len(l)):
        x=l[j]
        y=k//l[j]
        if x==y:
            calc1=0
            cnt=0
            for i in range(n):
                if a[i]==1:
                    cnt+=1
                else:
                    cnt=0
                if cnt>=x:
                    calc1+=1 
            cnt=0
            calc2=0
            for i in range(m):
                if b[i]==1:
                    cnt+=1
                else:
                    cnt=0
                if cnt>=y:
                    calc2+=1
            ans+=calc2*calc1  
        else:
            calc1=0
            cnt=0
            for i in range(n):
                if a[i]==1:
                    cnt+=1
                else:
                    cnt=0
                if cnt>=x:
                    calc1+=1 
            cnt=0
            calc2=0
            for i in range(m):
                if b[i]==1:
                    cnt+=1
                else:
                    cnt=0
                if cnt>=y:
                    calc2+=1
            ans+=calc2*calc1
            
            calc1=0
            cnt=0
            for i in range(n):
                if a[i]==1:
                    cnt+=1
                else:
                    cnt=0
                if cnt>=y:
                    calc1+=1 
            cnt=0
            calc2=0
            for i in range(m):
                if b[i]==1:
                    cnt+=1
                else:
                    cnt=0
                if cnt>=x:
                    calc2+=1
            ans+=calc2*calc1
    print(ans)        
        