Coordinate challenge

Use the clues about the symmetrical properties of these letters to place them on the grid.

Problem



Here is a grid:

 

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A 4-by-3 grid.



Can you position these ten letters in their correct places according to the eight clues below?

 

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The letters A, B, C, D, E.



 

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The letters P, S, X, Y, and Z.



Clues:

 

The letters at $(1, 1),$ $(1, 2)$ and $(1, 3)$ are all symmetrical about a vertical line.
 
The letter at $(4, 2)$ is not symmetrical in any way.
 
The letters at $(1, 1),$ $(2, 1)$ and $(3, 1)$ are symmetrical about a horizontal line.
 
The letters at $(0, 2),$ $(2, 0)$ have rotational symmetry.
 
The letter at $(3, 1)$ consists of just straight lines.
 
The letters at $(3, 3)$ and $(2, 0)$ consist of just curved lines.
 
The letters at $(3, 3),$ $(3, 2)$ and $(3, 1)$ are consecutive in the alphabet.
 
The letters at $(0, 2)$ and $(1, 2)$ are at the two ends of the alphabet.