During his long adventure, Steve stumbled upon a village of villagers. The houses in the village are connected by bidirectional paths. In total, there are (n) houses in the village, numbered from (1) to (n). The graph of houses and paths represents a rooted(^{\text{∗}}) tree(^{\text{†}}), rooted at vertex (1), where the town hall is located. Consider an arbitrary house (v) and its subtree(^{\text{‡}}). For each such house (v) and each non-negative integer (h), consider the set of houses that are in the subtree of (v) at a distance exactly (h) from (v). Such a set will be called a guild . For example, for (h=0), the guild will consist only of the vertex (v). In the example below, the guilds for the vertex (v=4) are shown. The guild for (h=0) is marked in red, for (h=1) in light blue, and for (h=2) in green. Two guilds are considered different if there exists a house that is in one guild and not in the other. Steve wants to know how many different non-empty guilds there are in the tree. Help him with this. (^{\text{∗}})A rooted tree is a tree where one vertex is special and called the root. (^{\text{†}})A tree is a connected graph without cycles. (^{\text{‡}})A subtree of vertex (v) is the subgraph of (v), all its descendants, and all the edges between them. 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) ((2 \le n \le 2 \cdot 10^5)) — the number of houses in the village. The second line contains (n-1) integers (p_2, p_3, \ldots, p_n) ((1 \le p_i \lt i)), where (p_i) is the parent of the (i)-th house in the tree. It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output a single integer — the n