CF869E The Untended Antiquity

Adieu l'ami. Koyomi is helping Oshino, an acquaintance of his, to take care of an open space around the abandoned Eikou Cram School building, Oshino's makeshift residence. The space is represented by a rectangular grid of $ n×m $ cells, arranged into $ n $ rows and $ m $ columns. The $ c $ -th cell in the $ r $ -th row is denoted by $ (r,c) $ . Oshino places and removes barriers around rectangular areas of cells. Specifically, an action denoted by " $ 1\ r_{1}\ c_{1}\ r_{2}\ c_{2} $ " means Oshino's placing barriers around a rectangle with two corners being $ (r_{1},c_{1}) $ and $ (r_{2},c_{2}) $ and sides parallel to squares sides. Similarly, " $ 2\ r_{1}\ c_{1}\ r_{2}\ c_{2} $ " means Oshino's removing barriers around the rectangle. Oshino ensures that no barriers staying on the ground share any common points, nor do they intersect with boundaries of the $ n×m $ area. Sometimes Koyomi tries to walk from one cell to another carefully without striding over barriers, in order to avoid damaging various items on the ground. " $ 3\ r_{1}\ c_{1}\ r_{2}\ c_{2} $ " means that Koyomi tries to walk from $ (r_{1},c_{1}) $ to $ (r_{2},c_{2}) $ without crossing barriers. And you're here to tell Koyomi the feasibility of each of his attempts.

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For the first example, the situations of Koyomi's actions are illustrated below.