Brave CHAIN

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.

Examples

Input

2 1 2 1 2 2 1

Output

2

Input

3 1 1 2 2 3 3 3 2 1

Output

1

Input

3 1 1 2 2 2 3 3 3 1

Output

3

inputFormat

Input

Input is given from Standard Input in the following format:

N A_1 A_2 \cdots A_{3N}

outputFormat

Output

Print the maximum number of points you can gain.

Examples

Input

2 1 2 1 2 2 1

Output

2

Input

3 1 1 2 2 3 3 3 2 1

Output

1

Input

3 1 1 2 2 2 3 3 3 1

Output

3

样例

3
1 1 2 2 2 3 3 3 1

3