Given an integer **N**, the task is to check if it is a Centered Octadecagonal number or not. Print “yes” if it is otherwise output is “no”.

Centered Octadecagonal numberrepresents a dot in the centre and others dot are arranged around it in successive layers of octadecagon(18 sided polygon). The first few Centered Octadecagonal numbers are 1, 19, 55, 109, 181, 271, 379, …

**Examples:**

Input:N = 19Output:YesExplanation:

19 is the Second Centered Octadecagonal number is 19.

Input:38Output:NoExplanation:

38 is not a Centered Octadecagonal number.

**Approach:** To solve the problem mentioned above we know that the K^{th} term of the Centered Octadecagonal number is given as:

As we have to check that the given number can be expressed as a Centered Octadecagonal number or not. This can be checked by generalizing the equation as:

=>

=>

Finally, check the value of computation using this formula if it is an integer, then it means that N is a Centered Octadecagonal number.

Below is the implementation of the above approach:

## C++

`// C++ implementation to check that` `// a number is a Centered` `// Octadecagonal number or not` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check that the` `// number is a Centered` `// Octadecagonal number` `bool` `isCenteredOctadecagonal(` `int` `N)` `{` ` ` `// Implement the formula generated` ` ` `float` `n = (9 + ` `sqrt` `(36 * N + 45)) / 18;` ` ` `// Condition to check if the` ` ` `// number is a Centered` ` ` `// Octadecagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 19;` ` ` `// Function call` ` ` `if` `(isCenteredOctadecagonal(n)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java implementation to check that` `// a number is a centered` `// octadecagonal number or not` `import` `java.lang.Math;` `class` `GFG{` ` ` `// Function to check that the` `// number is a centered` `// octadecagonal number` `public` `static` `boolean` `isCenteredOctadecagonal(` `int` `N)` `{` ` ` ` ` `// Implement the formula generated` ` ` `double` `n = (` `9` `+ Math.sqrt(` `36` `* N + ` `45` `)) / ` `18` `;` ` ` ` ` `// Condition to check if the` ` ` `// number is a Centered` ` ` `// Octadecagonal number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code ` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `19` `;` ` ` `// Function call` ` ` `if` `(isCenteredOctadecagonal(n))` ` ` `{` ` ` `System.out.println(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.println(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by divyeshrabadiya07` |

## Python3

`# Python3 implementation to check that` `# a number is a centered octadecagonal` `# number or not` `import` `math` `# Function to check that the` `# number is a centered` `# octadecagonal number` `def` `isCenteredOctadecagonal(N):` ` ` ` ` `# Implement the formula generated` ` ` `n ` `=` `(` `9` `+` `math.sqrt(` `36` `*` `N ` `+` `45` `)) ` `/` `18` `;` ` ` ` ` `# Condition to check if the` ` ` `# number is a centered` ` ` `# octadecagonal number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` `# Driver code` `if` `__name__` `=` `=` `'__main__'` `:` ` ` ` ` `n ` `=` `19` ` ` ` ` `# Function call` ` ` `if` `isCenteredOctadecagonal(n):` ` ` `print` `(` `'Yes'` `)` ` ` `else` `:` ` ` `print` `(` `'No'` `)` `# This code is contributed by rutvik_56` |

## C#

`// C# implementation to check that` `// a number is a centered` `// octadecagonal number or not` `using` `System;` `class` `GFG{` `// Function to check that the` `// number is a centered` `// octadecagonal number` `static` `bool` `isCenteredOctadecagonal(` `int` `N)` `{` ` ` `// Implement the formula generated` ` ` `double` `n = (9 + Math.Sqrt(36 * N + 45)) / 18;` ` ` ` ` `// Condition to check if the` ` ` `// number is a Centered` ` ` `// octadecagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` ` ` `// Driver Code` `static` `public` `void` `Main ()` `{` ` ` `int` `n = 19;` ` ` ` ` `// Function call` ` ` `if` `(isCenteredOctadecagonal(n))` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `}` `}` `}` `//This code is contributed by ShubhamCoder` |

## Javascript

`<script>` `// Javascript implementation to check that` `// a number is a Centered Octadecagonal` `// number or not` `// Function to check that the` `// number is a Centered` `// Octadecagonal number` `function` `isCenteredOctadecagonal(N)` `{` ` ` `// Implement the formula generated` ` ` `let n = parseInt((9 + Math.sqrt(36 * N + 45)) / 18);` ` ` `// Condition to check if the` ` ` `// number is a Centered` ` ` `// Octadecagonal number` ` ` `return` `(n - parseInt(n)) == 0;` `}` `// Driver Code` `let n = 19;` `// Function call` `if` `(isCenteredOctadecagonal(n))` `{` ` ` `document.write(` `"Yes"` `);` `}` `else` `{` ` ` `document.write(` `"No"` `);` `}` `// This code is contributed by souravmahato348` `</script>` |

**Output:**

Yes

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