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

||

6 | 1 | 8 |

7 | 5 | 3 |

2 | 9 | 4 |

||

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