Define the depth of a node in a rooted tree by applying the following rules recursively:
Let $S(T, d)$ be the number of nodes of $T$ with depth $d$. Two rooted trees $T$ and $T'$ are similar if and only if $S(T, d)$ equals $S(T', d)$ for all non-negative integer $d$.
You are given a rooted tree $T$ with $N$ nodes. The nodes of $T$ are numbered from 1 to $N$. Node 1 is the root node of $T$. Let $T_i$ be the rooted subtree of $T$ whose root is node $i$. Your task is to write a program which calculates the number of pairs $(i, j)$ such that $T_i$ and $T_j$ are similar and $i < j$.
The input consists of a single test case.
The first line contains an integer $N$ ($1 \leq N \leq 100,000$), which is the number of nodes in a tree. The following $N -1$ lines give information of branches: the $i$-th line of them contains $a_i$ and $b_i$, which indicates that a node $a_i$ is a parent of a node $b_i$. ($1 \leq a_i, b_i \leq N, a_i \ne b_i$) The root node is numbered by 1. It is guaranteed that a given graph is a rooted tree, i.e. there is exactly one parent for each node except the node 1, and the graph is connected.
Print the number of the pairs $(x, y)$ of the nodes such that the subtree with the root $x$ and the subtree with the root $y$ are similar and $x < y$.
5 1 2 1 3 1 4 1 5
6 1 2 2 3 3 4 1 5 5 6
13 1 2 1 3 2 4 2 5 3 6 3 7 4 8 4 9 6 10 7 11 8 12 11 13