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 sys
import math
import heapq
import collections
def inputnum():
    return(int(input()))
def inputnums():
    return(map(int,input().split()))
def inputlist():
    return(list(map(int,input().split())))
def inputstring():
    return([x for x in input()])
def inputmatrixchar(rows):
    arr2d = [[j for j in input().strip()] for i in range(rows)] 
    return arr2d
def inputmatrixint(rows):
    arr2d = []
    for _ in range(rows):
        arr2d.append([int(i) for i in input().split()])
    return arr2d

def get(a):
    rtn = []
    one = False
    cur = 0
    for i in range(len(a)):
        if a[i] == 1 and not one:
            one = True
        if a[i] == 1 and one:
            cur += 1 
        if a[i] == 0 and one:
            rtn.append(cur)
            cur = 0
            one = False
        elif i == len(a)-1 and cur > 0:
            rtn.append(cur)
    return rtn
    
n, m, k = inputnums()
a = inputlist()
b = inputlist()
length = get(a)
width = get(b)
ans = 0
i = 1
while i*i <= k:
    lengthcount = 0
    widthcount = 0
    if k%i == 0:
        for j in range(len(length)):
            if length[j] >= i:
                lengthcount += length[j]-i+1 
        for j in range(len(width)):
            if width[j] >= k//i:
                widthcount += width[j]-(k//i)+1
        ans += lengthcount*widthcount
        
        lengthcount = 0
        widthcount = 0
        if k != i*i:
            for j in range(len(length)):
                if length[j] >= k//i:
                    lengthcount += length[j]-k//i+1 
            for j in range(len(width)):
                if width[j] >= i:
                    widthcount += width[j]-i+1
            ans += lengthcount*widthcount
    i += 1
print(ans)