Problem Statement

We have $3N$ cards arranged in a row from left to right, where each card has an integer between $1$ and $N$ (inclusive) written on it. The integer written on the $i$-th card from the left is $A_i$.

You will do the following operation $N-1$ times:

• Rearrange the five leftmost cards in any order you like, then remove the three leftmost cards. If the integers written on those three cards are all equal, you gain $1$ point.

After these $N-1$ operations, if the integers written on the remaining three cards are all equal, you will gain $1$ additional point.

Find the maximum number of points you can gain.

Constraints

• $1 \leq N \leq 2000$
• $1 \leq A_i \leq N$

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_{3N}

Output

Print the maximum number of points you can gain.