Magical Square Checker

You are given a 3x3 grid of integers. Your task is to determine if the grid forms a magical square. A magical square is defined as a square in which the sum of the numbers in each row, each column, and both main diagonals are all equal. More formally, let the grid be represented as:

\( grid = \begin{bmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{bmatrix} \)

It is a magical square if:

• \( a_{11} + a_{12} + a_{13} = a_{21} + a_{22} + a_{23} = a_{31} + a_{32} + a_{33} \)
• \( a_{11} + a_{21} + a_{31} = a_{12} + a_{22} + a_{32} = a_{13} + a_{23} + a_{33} \)
• \( a_{11} + a_{22} + a_{33} = a_{13} + a_{22} + a_{31} \)

If the above conditions hold, output YES; otherwise, output NO.

inputFormat

The input consists of 3 lines, each line containing 3 space-separated integers representing a row of the grid.

For example:

8 1 6
3 5 7
4 9 2

outputFormat

Output a single line with YES if the given grid is a magical square, or NO otherwise.

## sample

8 1 6
3 5 7
4 9 2

YES