Given a number **N**, the task is to check if **N** is a Enneadecagonal Number or not. If the number **N** is an Enneadecagonal Number then print **“Yes”** else print **“No”**.

Enneadecagonal Numberis a 19-sided polygon in mathematics. It belongs to a class of figurative number. The number contains the number of dots and the dots are arranged in a pattern or series. An Enneadecagonal Number is also known as Nonadecagon. The dots have common points and all other dots are arrange in the successive layer. ThenthEnneadecagonal Number counts the seventeen number of dots and all the other dots are surrounding with a common sharing corner and make a pattern. The first few Enneadecagonal Numbers are1, 19, 54, 106, 175…

**Examples:**

Input:N = 19Output:YesExplanation:

Second Enneadecagonal Number is 19.

Input:N = 30Output:No

**Approach:**

1. The **K ^{th}** term of the Enneadecagonal Number is given as

2. As we have to check that the given number can be expressed as a **Enneadecagonal Number** or not. This can be checked as:

=>

=>

3. If the value of **K** calculated using the above formula is an integer, then **N** is a Enneadecagonal Number.

4. Else **N** is not a Enneadecagonal Number.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check if number N` `// is a enneadecagonal number` `bool` `isenneadecagonal(` `int` `N)` `{` ` ` `float` `n` ` ` `= (15 + ` `sqrt` `(136 * N + 225))` ` ` `/ 34;` ` ` `// Condition to check if N is a` ` ` `// enneadecagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given Number` ` ` `int` `N = 19;` ` ` `// Function call` ` ` `if` `(isenneadecagonal(N)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `class` `GFG{` `// Function to check if number N` `// is a enneadecagonal number` `static` `boolean` `isenneadecagonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `)(` `15` `+ Math.sqrt(` `136` `* N +` ` ` `225` `)) / ` `34` `;` ` ` `// Condition to check if N is a` ` ` `// enneadecagonal number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Given Number` ` ` `int` `N = ` `19` `;` ` ` `// Function call` ` ` `if` `(isenneadecagonal(N))` ` ` `{` ` ` `System.out.println(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.println(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by rutvik_56` |

## Python3

`# Python3 program for the above approach` `import` `math` `# Function to check if number N` `# is a enneadecagonal number` `def` `isenneadecagonal(N):` ` ` `n ` `=` `(` `15` `+` `math.sqrt(` `136` `*` `N ` `+` `225` `)) ` `/` `34` ` ` `# Condition to check if N is a` ` ` `# enneadecagonal number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` `# Driver Code` `N ` `=` `19` `# Function call` `if` `(isenneadecagonal(N)):` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` `# This code is contributed by divyamohan123` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` `// Function to check if number N` `// is a enneadecagonal number` `static` `bool` `isenneadecagonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `)(15 + Math.Sqrt(136 * N +` ` ` `225)) / 34;` ` ` ` ` `// Condition to check if N is a` ` ` `// enneadecagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` ` ` `// Driver Code` `static` `public` `void` `Main ()` `{` ` ` ` ` `// Given number` ` ` `int` `N = 19;` ` ` ` ` `// Function call` ` ` `if` `(isenneadecagonal(N))` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by shubhamsingh10` |

## Javascript

`<script>` `// Javascript program for the above approach` `// Function to check if number N` `// is a enneadecagonal number` `function` `isenneadecagonal(N){` ` ` `let n = parseFloat(15 + Math.sqrt(136 * N + 225)) / 34;` ` ` `// Condition to check if N is a` ` ` `//enneadecagonal number` ` ` `return` `(n - parseInt(n)) == 0` `}` `// Driver Code` `let N = 19;` `// Function call` `if` `(isenneadecagonal(N)){` ` ` `document.write(` `"Yes"` `);` ` ` `}` `else` `{` ` ` `document.write(` `"No"` `);` ` ` `}` `// This code is contributed by bobby` `</script>` |

**Output:**

Yes

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

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