## Tree Infection solution codeforces

A tree is a connected graph without cycles. A rooted tree has a special vertex called the root. The parent of a vertex vv (different from root) is the previous to vv vertex on the shortest path from the root to the vertex vv. Children of the vertex vv are all vertices for which vv is the parent. You are given a rooted tree with nn vertices. The vertex 11 is the root. Initially, all vertices are healthy. Each second you do two operations, the spreading operation and, after that, the injection operation:

- Spreading: for each vertex vv, if at least one child of vv is infected, you can spread the disease by infecting at most one other child of vv of your choice.
- Injection: you can choose any healthy vertex and infect it.

Input

The input consists of multiple test cases. The first line contains a single integer tt (1≤t≤1041≤t≤104) — the number of test cases. Description of the test cases follows. The first line of each test case contains a single integer nn (2≤n≤2⋅1052≤n≤2⋅105) — the number of the vertices in the given tree. The second line of each test case contains n−1n−1 integers p2,p3,…,pnp2,p3,…,pn (1≤pi≤n1≤pi≤n), where pipi is the ancestor if the ii-th vertex in the tree. It is guaranteed that the given graph is a tree. It is guaranteed that the sum of nn over all test cases doesn’t exceed 2⋅1052⋅105.Output

For each test case you should output a single integer — the minimal number of seconds needed to infect the whole tree.Example

input

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5 7 1 1 1 2 2 4 5 5 5 1 4 2 1 3 3 1 6 1 1 1 1 1

output

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4 4 2 3 4

Note

The image depicts the tree from the first test case during each second. A vertex is black if it is not infected. A vertex is blue if it is infected by injection during the previous second. A vertex is green if it is infected by spreading during the previous second. A vertex is red if it is infected earlier than the previous second.-
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