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>
def divisors(n):
    ind = 1
    arr = []
    while ind <= int(n**0.5):
        if n%ind == 0:
            if n//ind == ind:
                arr.append(ind)
            else:
                arr.append(ind)
                arr.append(n//ind)
        ind += 1
    arr.sort()
    return arr

n, m, k = list(map(int,input().split()))
row = list(map(int,input().split()))
col = list(map(int,input().split()))
div = divisors(k)
row_div = {}
col_div = {}

temp = [0]+row+[0]
cnt = 1
row_div[1] = temp.count(1)
for i in range(1, len(temp)):
    if temp[i]==temp[i-1] and temp[i]==1:
        cnt+=1
    else:
        count = 1
        while cnt>1:
            if cnt in row_div:
                row_div[cnt]+=count
            else:
                row_div[cnt]=count
            count+=1
            cnt-=1 
        cnt=1

temp = [0]+col+[0]
cnt = 1
col_div[1] = temp.count(1)
for i in range(1, len(temp)):
    if temp[i]==temp[i-1] and temp[i]==1:
        cnt+=1
    else:
        count = 1
        while cnt>1:
            if cnt in col_div:
                col_div[cnt]+=count
            else:
                col_div[cnt]=count
            count+=1
            cnt-=1 
        cnt=1

# print(row_div,col_div)
ans = 0
for i in div:
    cur = i
    nex = k // cur
    if cur in row_div and nex in col_div:
        ans += (row_div[cur]*col_div[nex])
print(ans)