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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class B {
	static int N, M, K;
	static int a[];
	static int b[];

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;

		st = new StringTokenizer(br.readLine());
		N = Integer.parseInt(st.nextToken());
		M = Integer.parseInt(st.nextToken());
		K = Integer.parseInt(st.nextToken());

		a = new int[N];
		b = new int[M];
		st = new StringTokenizer(br.readLine());
		for (int i = 0; i < N; i++) {
			a[i] = Integer.parseInt(st.nextToken());
		}
		st = new StringTokenizer(br.readLine());
		for (int j = 0; j < M; j++) {
			b[j] = Integer.parseInt(st.nextToken());
		}

		ArrayList<Integer> Ac = new ArrayList<Integer>();
		ArrayList<Integer> Bc = new ArrayList<Integer>();
		int maxA = 0;
		for (int i = 0; i < N; i++) {
			if (a[i] == 1) {
				int len = 0;
				while (i < N && a[i] == 1) {
					len++;
					i++;
				}
				maxA = Math.max(len, maxA);
				Ac.add(len);
			}
		}

		for (int i = 0; i < M; i++) {
			if (b[i] == 1) {
				int len = 0;
				while (i < M && b[i] == 1) {
					len++;
					i++;
				}
				Bc.add(len);
			}
		}

		// 조합 구하기
		long Answer = 0;
		for (int i = 1; i <= K; i++) {
			if(i>maxA)break;
			if (K % i == 0) {
				if (i <= N && K / i <= M) {
					int acnt =0;
					int bcnt =0;
					for(int tmp : Ac) {
						if(tmp>=i) {
							acnt+=tmp-i+1;
						}
					}
					for(int tmp : Bc) {
						if(tmp>=K/i) {
							bcnt+=tmp-K/i+1;
						}
					}
					Answer+=acnt*bcnt;
				}
			}
		}
		System.out.println(Answer);
	}
}
