Problem: 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

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.buffer.readline

n = int(input())
a = list(map(int,input().split()))

a.append(n+1)
a.append(n+1)

dp = [[-1]*(n+2) for i in range(n+2)]
ma = [-1]*(n+2)

dp[a[0]][a[1]] = 0
ma[a[0]] = 0
ma[a[1]] = 0

after = 0

for i in range(n):
    x,y,z = a[3*i+2],a[3*i+3],a[3*i+4]
    if x == z:
        y,z = z,y
    if y == z:
        x,z = z,x
    
    if x == z:
        after += 1
        continue

    
    tank = []

    if x != y:
        for i in range(n+1):
            tank.append((i,x,ma[i]))
            tank.append((i,y,ma[i]))
            tank.append((i,z,ma[i]))       
        tank.append((x,y,max(max(ma),dp[z][z] + 1)))
        tank.append((x,z,max(max(ma),dp[y][y] + 1)))
        tank.append((y,z,max(max(ma),dp[x][x] + 1)))
    else:
        for i in range(n+1):
            tank.append((i,x,ma[i]))
            tank.append((i,y,ma[i]))
            tmp = ma[i]
            if dp[i][x] != -1:
                tmp = max(tmp,dp[i][x] + 1)
            if dp[x][i] != -1:
                tmp = max(tmp,dp[x][i] + 1)
            tank.append((i,z,tmp))
        tank.append((x,y,max(max(ma),dp[z][z] + 1)))
        tank.append((x,z,max(max(ma),dp[y][y] + 1)))
        tank.append((y,z,max(max(ma),dp[x][x] + 1)))

    for p,q,c in tank:
        dp[p][q] = max(dp[p][q],c)
        ma[p] = max(ma[p],c)
        ma[q] = max(ma[q],c)

res = 0
for i in range(n+2):
    for j in range(n+2):
        res = max(res,dp[i][j])

print(res+after)