This page is still under construction.

Parts of this page are still being built. What you see may change.

Magic Squares

Interview

Time limit1sMemory limit256 MB

Summary
Check each test case square by comparing every row, column, and both diagonal sums and report whether it is magic.
Level

Easy2 of 10

Topics
Matrix, Simulation
Solved
No attempts yet

Problem

A magic square is an arrangement of integers in a square grid where the sum of each row, each column, and both main diagonals is the same. The grid has equal numbers of rows and columns. Let mm denote the side length, so the square contains m2m^2 integers. The figure below shows a magic square with m=3m=3.

Input

The first line contains a positive integer nn, the number of test cases. Each test case begins with an integer mm, the side length of the square. The next mm lines each contain mm integers separated by one or more spaces.

Output

For each test case, if the square is a magic square, print Magic square of size m, where mm is the number of rows. Otherwise print Not a magic square.

Constraints

  • 2≤m≤52 \leq m \leq 5

Examples3

  1. Example 1

    Input
    4
3
2 7 6
9 5 1
4 3 8
2
14 22
26 10
4
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
2
5 5
5 5
    Expected output
    Magic square of size 3
Not a magic square
Magic square of size 4
Magic square of size 2

  2. Example 2

    Input
    1
3
8 1 6
3 5 7
4 9 2
    Expected output
    Magic square of size 3

  3. Example 3

    Input
    1
2
1 2
3 4
    Expected output
    Not a magic square