2c:T52d,

Art critics worldwide have only recently begun to recognize the creative genius behind the great bovine painter, Picowso.

Picowso paints in a very particular way. She starts with an $N \times N$ blank canvas, represented by an $N \times N$ grid of zeros, where a zero indicates an empty cell of the canvas. She then draws $N^2$ rectangles on the canvas, one in each of $N^2$ colors (conveniently numbered $1 \ldots N^2$). For example, she might start by painting a rectangle in color 2, giving this intermediate canvas:

She might then paint a rectangle in color 7:

And then she might paint a small rectangle in color 3:

Each rectangle has sides parallel to the edges of the canvas, and a rectangle could be as large as the entire canvas or as small as a single cell. Each color from $1 \ldots N^2$ is used exactly once, although later colors might completely cover up some of the earlier colors.

Given the final state of the canvas, please count how many of the $N^2$ colors could have possibly been the first to be painted.

2d:T72d,

세계 각국의 미술 비평가들은 '비앙끄'로 알려진 훌륭한 화가 정숙의 창의성에 주목하기 시작했습니다.

정숙은 매우 특별한 방식으로 그림을 그립니다. 그녀는 처음에 $N \times N$ 크기의 빈 캔버스에 시작하는데, 이는 $N \times N$ 격자로 표현되며 각 셀에는 0이 들어가 있고, 이것은 공백 셀을 나타냅니다.

그녀는 이후에 $N^2$개의 사각형을 캔버스 위에 그리는데, 각각 $N^2$개의 색상 중 하나로 그립니다 (

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