Count Balanced Nodes in a Tree

You are given a tree rooted at node 1. A node is balanced if the subtrees of all its direct children have the same size; leaf nodes are considered balanced as stated in the problem. Output the total number of balanced nodes. This site supplements the parent-list input protocol and the size limits.

输入格式

The first line contains n (1≤n≤200000); the second line contains n−1 integers, the parent labels of nodes 2..n in order (1-based). When n=1, the second line may be empty. The input is guaranteed to form a tree rooted at node 1.

输出格式

Output the number of balanced nodes.

样例 1

输入：

1

输出：

1

样例 2

输入：

4
1 2 3

输出：

4

样例 3

输入：

4
1 1 2

输出：

3