Little Elephant and Magic Square · Interview Problem

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Codeforces

Easy

Arrays

Matrices

Simulation

Little Elephant and Magic Square

Determine whether a small square grid is an odd-sized magic square: all rows, columns, and diagonals have the same sum.

Acceptance 0%

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Problem Statement

Problem

You are given an $n \times n$ square grid of integers. Your task is to determine whether the grid is a magic square.

A square grid is considered a magic square if:

the sums of all rows are equal,
the sums of all columns are equal,
the sums of the two main diagonals are equal,
and all of these sums are the same value.

For this problem, the grid is small enough that direct checking of all required sums is sufficient.

Goal

Return whether the provided square grid satisfies the magic square condition.

Input Format

The first line contains an integer $n$ .
The next $n$ lines contain $n$ integers each, describing the grid.

Output Format

Print YES if the grid is a magic square.
Otherwise, print NO.

Constraints

$1 \le n$
The grid is square with $n$ rows and $n$ columns.
Integer values fit in standard 32-bit signed range.
A direct $O(n^2)$ check is sufficient.

Examples

Sample cases returned by the problem API.

Example 1

Input

Output

YES

Explanation

Every row, column, and both diagonals sum to 15.

Example 2

Input

Output

NO

Explanation

The row sums are all 6, 15, and 24, so the grid is not a magic square.

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