{"problem":{"name":"Brave CHAIN","description":{"content":"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 $A_i$. Y","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc176_f"},"statements":[{"statement_type":"Markdown","content":"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 $A_i$.\nYou will do the following operation $N-1$ times:\n\n*   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.\n\nAfter these $N-1$ operations, if the integers written on the remaining three cards are all equal, you will gain $1$ additional point.\nFind the maximum number of points you can gain.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2000$\n*   $1 \\leq A_i \\leq N$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\cdots$ $A_{3N}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc176_f","tags":[],"sample_group":[["2\n1 2 1 2 2 1","2\n\nLet 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.\nThen, remove the three leftmost cards, all of which have the same integer $2$, gaining $1$ point.\nNow, the integers written on the remaining cards are $1\\ 1\\ 1$.\nSince these three cards have the same integer $1$, we gain $1$ more point.\nIn this way, we can gain $2$ points - which is the maximum possible."],["3\n1 1 2 2 3 3 3 2 1","1"],["3\n1 1 2 2 2 3 3 3 1","3"]],"created_at":"2026-03-03 11:01:14"}}