Problem Statement

Given is a tree with $N$ vertices. The vertices are numbered $1,2,\ldots,N$, and the $i$-th edge $(1 \leq i \leq N-1)$ connects Vertex $u_i$ and Vertex $v_i$.

Find the number of integers $i$ $(1 \leq i \leq N)$ that satisfy the following condition.

• The size of the maximum matching of the graph obtained by deleting Vertex $i$ and all incident edges from the tree is equal to the size of the maximum matching of the original tree.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq u_i < v_i \leq N$
• The given graph is a tree.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
u_1 v_1
u_2 v_2
\vdots
u_{N-1} v_{N-1}

Output

Print the answer.