Magic squares P99555
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 32 = 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 n2. 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