You are given a full binary tree(^{\text{∗}}) of (n) nodes, rooted at node (1). For each node (u) ((1\le u\le n)), we define function (f_u : \mathbb R_+ \to \mathbb R_+) as follows: If (u) is a leaf(^{\text{†}}), then (f_u(x)=x); Otherwise, denote the left child of (u) as (l_u) and the right child of (u) as (r_u), then (f_u(x)=(f_{l_u}(x))^{f_{r_u}(x)}). For two nodes (u) and (v), we say (u\prec v) if and only if one of the following holds: (f_{u}(x) N), (f_u(x) < f_v(x)) holds. The same is defined for (f_u(x) = f_v(x)) when (x\to \infty). (^{\text{§}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). 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 a single integer (n) ((1\le n \le 4\cdot 10^5), (n) is odd) — the size of the full binary tree. Then (n) lines follow, the (i)-th line containing two integers (l_i) and (r_i) ((0\le l_i, r_i\le n)) — the left child and the right child of node (i). If (i) is a leaf, then (l_i=r_i=0). It is guaranteed that the given input forms a full binary tree rooted at node (1). It is guaranteed that the sum of (n) over all test cases does not exceed (4\cdot 10^5). For each test case, output (n) integers (p_1, p_2, \ldots, p_n) ((1\le p_i\le n), all (p_i) are distinct) — the permutation you found. You need to guarantee that for each (1\le i < n), (p_i\prec p_{i+1}). In the first test case, (f_2(x)=f_3(x)=x), and