Arpa's weak amphitheater and Mehrdad's valuable Hoses

Description:

Input:

The first line contains integers n, m and w (1  ≤  n  ≤  1000, , 1 ≤ w ≤ 1000) — the number of Hoses, the number of pair of friends and the maximum total weight of those who are invited.

The second line contains n integers w₁, w₂, ..., w_n (1 ≤ w_i ≤ 1000) — the weights of the Hoses.

The third line contains n integers b₁, b₂, ..., b_n (1 ≤ b_i ≤ 10⁶) — the beauties of the Hoses.

The next m lines contain pairs of friends, the i-th of them contains two integers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i), meaning that Hoses x_i and y_i are friends. Note that friendship is bidirectional. All pairs (x_i, y_i) are distinct.

Output:

Print the maximum possible total beauty of Hoses Mehrdad can invite so that no one gets hurt and the total weight doesn't exceed w.

Sample Input:

3 1 5
3 2 5
2 4 2
1 2

Sample Output:

6

Sample Input:

4 2 11
2 4 6 6
6 4 2 1
1 2
2 3

Sample Output:

7

Note:

In the first sample there are two friendship groups: Hoses {1, 2} and Hos {3}. The best way is to choose all of Hoses in the first group, sum of their weights is equal to 5 and sum of their beauty is 6.

In the second sample there are two friendship groups: Hoses {1, 2, 3} and Hos {4}. Mehrdad can't invite all the Hoses from the first group because their total weight is 12 > 11, thus the best way is to choose the first Hos from the first group and the only one from the second group. The total weight will be 8, and the total beauty will be 7.