Once, a messenger of the sultan found a wall with this square filled with numbers:

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6 | 1 | 8 |

7 | 5 | 3 |

2 | 9 | 4 |

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Asked, Beremiz told the sultan
that it was a “magic square” of order 3,
that is, a square of size 3,
where all the numbers between 1 and 3^{2} = 9 appear once,
and where all the rows, all the columns
and the two diagonals add up to the same number,
15 in the example.

Input

Input consists of several cases,
each with the order n of a square,
followed by n rows,
each with n natural numbers between 1 and n^{2}.
Assume 1 ≤ n ≤ 100.

Output

For every case, print “yes” if the given square is magic, and “no” otherwise.

Public test cases

**Input**

3 6 1 8 7 5 3 2 9 4 3 6 1 8 7 5 9 2 3 4 3 1 6 8 5 7 3 9 2 4 1 1 2 1 2 3 4 4 4 5 16 9 14 11 2 7 1 8 13 12 15 10 3 6

**Output**

yes no no yes no yes

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Spanish
- Other languages
- Spanish
- Official solutions
- C++ Python
- User solutions
- C++ Java Python