Problem:
Score : 600 points

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.

Sample Input 1

2
1 2 1 2 2 1

Sample Output 1

2

Let us rearrange the five leftmost cards so that the integers written on the six cards will be 2\ 2\ 2\ 1\ 1\ 1 from left to right.

Then, remove the three leftmost cards, all of which have the same integer 2, gaining 1 point.

Now, the integers written on the remaining cards are 1\ 1\ 1.

Since these three cards have the same integer 1, we gain 1 more point.

In this way, we can gain 2 points - which is the maximum possible.

Sample Input 2

3
1 1 2 2 3 3 3 2 1

Sample Output 2

1

Sample Input 3

3
1 1 2 2 2 3 3 3 1

Sample Output 3

3

Solution in PyPy3 (7.3.0) (judge verdict: Wrong Answer)

n = int(input())
A = list(map(lambda x:int(x)-1,input().split()))

two = [0]*n
one = [0]*n

two[A[0]] += 1
two[A[1]] += 1

ans = 0
for i in range(n-1):
    nxt = A[3*i+2:3*i+5]
    nxt.sort()
    if nxt[0] == nxt[1] == nxt[2]:
        ans += 1
        continue
    if nxt[1] == nxt[2]:
        nxt.reverse()
    if nxt[0] == nxt[1]:
        if one[nxt[0]] >= 1:
            ans += 1
            one = two[:]
            two = [0]*n
            two[nxt[2]] += 1
            continue
        if two[nxt[0]] >= 1:
            ans += 1
            two[nxt[0]] -= 1
            for i in range(n):
                one[i] += two[i]
            two = [0]*n
            two[nxt[2]] += 1
            continue
        if two[nxt[2]] >= 1 and two[nxt[2]] + one[nxt[2]] >= 2:
            ans += 1
            two = [0]*n
            one = [0]*n
        else:
            two[nxt[2]] += 1
        two[nxt[0]] += 2
        continue
    if two[nxt[0]] >= 1 and two[nxt[0]] + one[nxt[0]] >= 2:
        ans += 1
        two = [0]*n
        one = [0]*n
        two[nxt[1]] += 1
        two[nxt[2]] += 1
        continue
    if two[nxt[1]] >= 1 and two[nxt[1]] + one[nxt[1]] >= 2:
        ans += 1
        two = [0]*n
        one = [0]*n
        two[nxt[0]] += 1
        two[nxt[2]] += 1
        continue
    if two[nxt[2]] >= 1 and two[nxt[2]] + one[nxt[2]] >= 2:
        ans += 1
        two = [0]*n
        one = [0]*n
        two[nxt[1]] += 1
        two[nxt[0]] += 1
        continue
    for i in range(3):
        two[nxt[i]] += 1
if two[A[-1]] >= 1 and one[A[-1]] + two[A[-1]]>= 2:
    ans += 1
print(ans)