Bob lives in a country called HackerLand and in this country, there are $N$ cities numbered $1$ to $N$ and they form a tree. That is, there are $N - 1$ undirected roads between these $N$ cities and every two cities can reach each other through these roads. The length of the road between city $i$ and city $j$ is $(i + j)$ (meaning if there is a road between city $i$ and city $j$ then the length will be $i + j$).

So a great scientist in HackerLand invented the new car in which Bob can travel from one city to another city in $f(i, j)$ time where $f(i, j)$ indicates bitwise xor of length of the roads in the simple path between city $i$ and $j$. So Bob was curious to find the bitwise xor of all $f(i, j)$ such that  $1 \leq i \lt j \leq N$. Help Bob to find.

For example, if our country has $4$ cities then we have to find  $f(1,2) ⊕ f(1,3) ⊕ f(1,4) ⊕ f(2,3) ⊕ f(2,4) ⊕ f(3,4)$ where $\oplus$ denotes bitwise xor operator.

Input Format

• The first line contains $N$, the number of cities in the country.
• Then $N - 1$ lines contains two integers $u$ and $v$, means that there is a undirected road between city $u$ and city $v$. It is guaranteed that the given roads form a tree.

Output Format

Print a single integer denoting our answer

Constraints

$1 \leq N \leq 10^5 \\ 1 \leq u, v \leq N$

Note: The country HackerLand has a tree structure