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>
'''Author- Akshit Monga'''
from sys import stdin, stdout
input = stdin.readline
import math
t = 1
for _ in range(t):
    n,m,k=map(int,input().split())
    a=[int(x) for x in input().split()]
    b=[int(x) for x in input().split()]
    vals=[]
    p=0
    c=0
    for i in b:
        if p==0:
            if i:
                c=1
                p=1
        else:
            if i:
                c+=1
            else:
                if c:
                    vals.append(c)
                p=0
                c=0
    if c:
        vals.append(c)
    vals2 = []
    p = 0
    c = 0
    for i in a:
        if p == 0:
            if i:
                c = 1
                p = 1
        else:
            if i:
                c += 1
            else:
                if c:
                    vals2.append(c)
                p = 0
                c = 0
    if c:
        vals2.append(c)
    ans=0
    p1=[0 for i in range(m+1)]
    p2=[0 for i  in range(n+1)]
    for i in vals:
        for j in range(1,i+1):
            p1[j]+=(i-j+1)
    for i in vals2:
        for j in range(1, i + 1):
            p2[j] += (i - j + 1)
    i = 1
    while i <= math.sqrt(k):
        if (k % i == 0):
            if (k // i == i):
                a = b = i
                if a<=m and b<=n:
                    ans += p1[a]*p2[b]
            else:
                a = i
                b = k // i
                if a<=m and b<=n:
                    ans += p1[a]*p2[b]
                a,b=b,a
                if a<=m and b<=n:
                    ans += p1[a]*p2[b]
                a,b=b,a
        i = i + 1
    print(ans)