2448 - Magic Matrix - PK@Contest.bjtu

2448.Magic Matrix

Time Limit: 1s Memory Limit: 256MB

You're given a matrix A of size n \times n.

Let's call the matrix with nonnegative elements magic if it is symmetric (so aij=aji), aii=0 and aij \le max(aik,ajk) for all triples i,j,k. Note that i,j,k do not need to be distinct.

Determine if the matrix is magic.

As the input/output can reach very huge size it is recommended to use fast input/output methods: for example, prefer to use scanf/printf instead of cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.

Input Format(From the terminal/stdin)

The first line contains integer n (1 \le n \le 2500) - the size of the matrix A.

Each of the next n lines contains n integers aij (0 \le aij \lt 109) - the elements of the matrix A.

Note that the given matrix not necessarily is symmetric and can be arbitrary.

Output Format(To the terminal/stdout)

Print ''MAGIC" (without quotes) if the given matrix A is magic. Otherwise print ''NOT MAGIC".

Sample Input 1

Copy

3
0 1 2
1 0 2
2 2 0
 \n
 · · \n
 · · \n
 · · \n

Sample Output 1

Copy

MAGIC
     \n

Sample Input 2

Copy

2
0 1
2 3
 \n
 · \n
 · \n

Sample Output 2

Copy

NOT MAGIC
   ·     \n

Sample Input 3

Copy

4
0 1 2 3
1 0 3 4
2 3 0 5
3 4 5 0
 \n
 · · · \n
 · · · \n
 · · · \n
 · · · \n

Sample Output 3

Copy

NOT MAGIC
   ·     \n

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