Problem Statement

We have $N$ cards numbered $1$ to $N$. Each side of each card has a color represented by a positive integer.

One side of Card $i$ has a color $a_i$, and the other side has a color $b_i$.

For each card, you can choose which side shows up. Find the maximum possible number of different colors showing up.

Constraints

• $1 \leq N \leq 200000$
• $1 \leq a_i,b_i \leq 400000$
• All numbers in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
a_2 b_2
:
a_N b_N

Output

Print the answer.