$N \times N$ 크기의 격자 $A$ 가 주어집니다. 가장 왼쪽 위 칸의 위치를 $ (0,0) $ 으로 정의합니다.
이때 왼쪽 위 칸에서 아래로 $i \ (0 \leq i \leq N-1) $ 칸, 오른쪽으로 $j \ (0 \leq j \leq N-1) $ 칸 이동한 위치는 $ (j, i) $ 로 나타냅니다.
각 칸에는 정수가 적혀 있으며, 위치 $ (j, i) $ 의 칸에 적힌 정수를 $A_{i,j}$ 로 나타냅니다.
모든 칸의 정수가 0인 상태를 "초기 격자"라고 정의합니다.
격자 $P$ 에 대한 "산 모양 더하기" $ (X, Y, H) $ 를 다음과 같이 정의합니다.

• 먼저 산의 중심이 될 칸의 위치 $ (X, Y) \ (0 \leq X, Y \leq N-1) $ 와 산의 높이를 나타내는 정수 $H \ (1 \leq H \leq N) $ 를 지정합니다.
• 그 후 모든 칸의 $P_{y,x}$ 를 $P_{y,x} + \max(0, H - |x-X| - |y-Y|) $ 로 바꿉니다.

주어진 격자 $A$ 는 초기 격자에 산 모양 더하기를 1000번 수행하여 생성된 격자입니다.
당신의 목적은 격자 $A$ 에 최대한 가까운 격자를 생성하는 산 모양 더하기 순서를 구하는 것입니다.
격자 $A$ 와 생성된 격자 $B$ 의 차이를 최소화하는 조작 순서를 구하세요.


[제약 조건]
• $1 \le H, W \le 40$
• $H, W$ 는 정수

$N \times N$ 크기의 격자 데이터 $A_{i,j}$ 가 주어집니다.

수행할 산 모양 더하기 $ (X, Y, H) $ 를 최대 1000줄에 걸쳐 출력하세요.

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