For a set of pairs (S = \{(a_1, b_1), (a_2, b_2), \ldots, (a_m, b_m)\}), where (a_i < b_i) for all (1 \le i \le m), we define (f(S)) and (g(S)) as follows: Treating each ((a_i, b_i)) as a segment on the number line, (f(S)) is the length of their union. Formally, (f(S)) is the number of integers (x) such that there exists an (i) ((1 \leq i \leq m)) where (x, x+1 \subseteq a_i, b_i). Treating each ((a_i, b_i)) as an undirected edge in a graph, (g(S)) is the number of nodes that lie on at least one simple cycle with at least (3) edges. Formally, (g(S)) is the number of nodes (x_1) such that there exists a path (x_1 \to x_2 \to \ldots \to x_k \to x_1) in the graph, where (k \geq 3) and all (x_1, x_2, \ldots, x_k) are distinct. For example, (S = \{(1,2), (2,4), (1,4), (4,5),(6,7)\}), we can get (f(S) = 5) and (g(S) = 3). You are given (n) distinct pairs. Your task is to select a subset (S') of these pairs such that (f(S') - g(S')) is maximized. You need to output the indices of the selected pairs. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains an integer (n) ((1 \le n \le 3 \cdot 10^3)). Next (n) lines each contain two integers (a_i) and (b_i) ((1 \le a_i < b_i \le 2n)), representing a pair. It is guaranteed that all pairs are distinct within the same test case. It is guaranteed that the sum of (n^2) over all test cases will not exceed (9 \cdot 10^6). For each test case, the first line contains an integer (k) ((0 \le k \le n)) — the size of the subset (S'). Next line contains (k) integers (i_1, i_2, \ldots, i_m) ((1 \le i_1 , i_2 , \ldots , i_k \le n)) — the indices of the selected pairs. Note the indices must be distinct . In the first test