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>
from sys import stdin, stdout
def cnt(s):
    ans = []
    temp = 0
    for i in range(len(s)-1):
        if s[i]==1 and s[i+1]==1:
            temp+=1
        elif s[i]==1 and s[i+1]==0:
            ans.append(temp+1)
            temp = 0
    if s[len(s)-1]==1:
        ans.append(temp+1)
    return ans
n, m, k = map(int, stdin.readline().split())
col = list(map(int, stdin.readline().split()))
row = list(map(int, stdin.readline().split()))
fac = []
i = 1
while(i*i<=k):
    if k%i==0:
        fac.append([i, k//i])
    i+=1
ans = 0
co = cnt(col)
ro = cnt(row)
co.sort(reverse=True)
ro.sort(reverse=True)
for i in range(len(fac)):
    if fac[i][0]==fac[i][1]:
        t1 = 0
        t2 = 0
        for j in range(len(co)):
            if(co[j]>=fac[i][0]):
                t1+=co[j]-fac[i][0]+1
            else:
                break
        for j in range(len(ro)):
            if (ro[j] >= fac[i][0]):
                t2 += ro[j] - fac[i][0] + 1
            else:
                break
        ans+=t1*t2
    else:
        t1 = 0
        t2 = 0
        for j in range(len(co)):
            if (co[j] >= fac[i][0]):
                t1 += co[j] - fac[i][0] + 1
            else:
                break
        for j in range(len(ro)):
            if (ro[j] >= fac[i][1]):
                t2 += ro[j] - fac[i][1] + 1
            else:
                break
        ans+=t1*t2
        t1 = 0
        t2 = 0
        for j in range(len(co)):
            if (co[j] >= fac[i][1]):
                t1 += co[j] - fac[i][1] + 1
            else:
                break
        for j in range(len(ro)):
            if (ro[j] >= fac[i][0]):
                t2 += ro[j] - fac[i][0] + 1
            else:
                break
        ans+=t1*t2
stdout.write(str(ans)+"\n")