Tree

Problem Description

You are given a tree consisting of $n$ vertices numbered $1$ to $n$ rooted at node $1$. The parent of the $i$-th vertices is $p_i$. You can move from a vertex to any of its children. What's more, you can add one directed edge between any two different vertices, and you can move through this edge too. You need to maximize the number of pairs $(x,y)$ such that $x$ can move to $y$ through the edges after adding the edge. Note that $x$ can also move to $x$.

Input

The first line contains one integer $T$ $(1\leq T\leq 100000)$ — the number of test cases. The first line of each test case contains only one integer $n(1\leq n\leq 5\times 10^5)$ — the number of vertices in the tree. The second line of each test case contains $n-1$ integers $p_2,p_3,\dots,p_n (1\leq p_i<i)$ — the parent of each non-root node. The sum of $n$ over all test cases does not exceed $10^6$.

Output

Print $T$ integers — for each test case output the maximum number of pairs $(x,y)$ that vertices $x$ can move to $y$ after adding one edge.

Sample Input

2
5
1 1 2 2
6
1 2 3 1 3

Sample Output

17
26

Source

2020 Multi-University Training Contest 9