Monocarp has (n) friends and decided to give a New Year's gift to each of them. He has also prepared (m) boxes to place the gifts in; the beauty of the (i)-th box is (a_i). Every box can contain at most one gift. Monocarp wants to give a gift worth at least (y_i) coins to the (i)-th friend. Additionally, he knows that the (i)-th friend will be happy if at least one of the following conditions holds: the gift is in a box with beauty at least (x_i); the gift is worth at least (z_i) ((z_i > y_i)). Your task is to help Monocarp calculate the maximum possible number of friends he can make happy if he has (k) coins. Note that Monocarp must purchase a gift for each friend, and the gift may not necessarily come in a box . The first line contains a single integer (t) ((1 \le t \le 10^4)) — the number of test cases. The first line of each test case contains three integers (n), (m) and (k) ((1 \le n, m \le 2 \cdot 10^5); (1 \le k \le 10^{15})). The second line contains (m) integers (a_1, a_2, \dots, a_m) ((1 \le a_i \le m)). Then (n) lines follow; the (i)-th of them contains three integers (x_i), (y_i) and (z_i) ((1 \le x_i \le m); (1 \le y_i < z_i \le 10^9)). Additional constraints on the input: (\sum\limits_{i=1}^{n} y_i \le k). the sum of (n) over all test cases doesn't exceed (2 \cdot 10^5); the sum of (m) over all test cases doesn't exceed (2 \cdot 10^5); For each test case, print a single integer — the maximum possible number of friends Monocarp can make happy if he has (k) coins. In the first example, Monocarp can make both friends happy as follows: give the first friend a gift for (3) coins, and give the second friend a gift for (2) coins in a box with (1) beauty. In the second example, Monocarp cannot make any of his friends happy, because he does not have enough money to buy a gift for (z_i) coins for even o