Check if a number is perfect (sum of factors equals number).

Difficulty: Hard

Phase: 6 · Mixed Logical Challenges

XP Reward: 30 XP

Topics: Mixed Logical Challenges, Hard

Supported Languages: Python, JavaScript, C, C++, Java

Problem Description

Given N, print concentric square pattern of numbers of size (2N-1) x (2N-1). Input Format: Read input from standard input (stdin). Output Format: Print the result to standard output (stdout).

Constraints

-10^9 <= N <= 10^9

Examples

Example 1

Input: 2

Output: 2 2 2 2 1 2 2 2 2

Explanation: Sample execution for input 2