시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 1024 MB32618816157.295%

문제

$N \times N \times N$ 크기의 입체 공간이 있다. 공간 속 좌표는 $1 \leq i,j,k \leq N$을 만족하는 세 정수 $(i,j,k)$로 나타낸다.

공간 속에는 $M$개의 큐브들이 존재하며, 각 큐브는 정확히 하나씩의 좌표를 차지한다. 같은 좌표에는 여러 개의 큐브가 겹쳐 있지 않다. 다음 조건을 만족하는 큐브의 개수를 찾아보자.

  • $(i,j,k)$에 큐브가 존재할 때, $(i\pm1,j,k), (i,j\pm1,k), (i,j,k\pm1)$ 총 $6$곳 모두에 큐브가 존재한다.

입력

첫 번째 줄에 두 정수 $N$, $M$이 주어진다.

다음 $M$개의 줄에 걸쳐 각 줄마다 세 정수 $i$, $j$, $k$가 주어진다. 이는 $(i,j,k)$에 큐브가 존재한다는 의미이다.

출력

문제의 정답을 출력한다.

제한

  • $3 \leq N \leq 5$
  • $0 \leq M \leq N^3$
  • $1 \leq i,j,k \leq N$
  • 중복된 좌표는 주어지지 않음

예제 입력 1

3 1
1 1 1

예제 출력 1

0

조건을 만족하는 큐브는 없다.

예제 입력 2

3 7
2 2 2
1 2 2
3 2 2
2 1 2
2 3 2
2 2 1
2 2 3

예제 출력 2

1

$(2,2,2)$에 있는 큐브는 조건을 만족하므로, 조건을 만족하는 큐브는 $1$개이다.

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