Given a "balanced" (not sure) binary tree. Find the lucky quadruplets, which is definied as an unordered set of 4 nodes such that all the nodes in the set are distinct and we can choose a node from that set to be the centre such that the distance of the other 3 nodes from the selected node is the same.

Input Format:

- The first line contains an integer N denoting the number of nodes in the tree
- Then next line contains N space separated integers denoting the parent array where : parent[i] is the parent of the node i
- You may assume that the given parent array corresponds to a balanced binary tree.

Constraints

Sample Input

7

0112233

Sample Output

6