Given an integer **N**, the task is to check if it is a Icosagonal Number or not. If the number **N** is an Icosagonal Number then print **“YES”** else print **“NO”**.

Icosagonal Numberis a twenty-sided polygon. The number derived from the figurative class. There are different patterns observed in this series. The dots are countable, arrange in a specific way of position, and create a diagram. All the dots have common dots points, all other dots are connected to these points and except this common point the dots connected to their ith dots with their respective successive layer… The first few Icosagonal numbers are1, 20, 57, 112, 185, 276…

**Examples:**

Input:N = 20Output:YesExplanation:

Second Icosagonal Number is 20.

Input:N = 30Output:No

**Approach:**

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

2. As we have to check that the given number can be expressed as a icosagonal number or not. This can be checked as follows –

=>

=>

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

4. Else the number **N** is not an Icosagonal 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 the number` `// N is a icosagonal number` `bool` `iicosagonal(` `int` `N)` `{` ` ` `float` `n` ` ` `= (16 + ` `sqrt` `(144 * N + 256))` ` ` `/ 36;` ` ` `// Condition to check if the` ` ` `// N is a icosagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given Number` ` ` `int` `N = 20;` ` ` `// Function call` ` ` `if` `(iicosagonal(N)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` `// Function to check if the number` `// N is a icosagonal number` `static` `boolean` `iicosagonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `)((` `16` `+ Math.sqrt(` `144` `* N +` ` ` `256` `)) / ` `36` `);` ` ` `// Condition to check if the` ` ` `// N is a icosagonal number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Given Number` ` ` `int` `N = ` `20` `;` ` ` `// Function call` ` ` `if` `(iicosagonal(N))` ` ` `{` ` ` `System.out.print(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.print(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by Rohit_ranjan` |

## Python3

`# Python3 program for the above approach` `import` `numpy as np` `# Function to check if the number` `# N is a icosagonal number` `def` `iicosagonal(N):` ` ` `n ` `=` `(` `16` `+` `np.sqrt(` `144` `*` `N ` `+` `256` `)) ` `/` `36` ` ` `# Condition to check if the` ` ` `# N is a icosagonal number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` `# Driver Code` `N ` `=` `20` `# Function call` `if` `(iicosagonal(N)):` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` `# This code is contributed by PratikBasu` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` `// Function to check if the number` `// N is a icosagonal number` `static` `bool` `iicosagonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `)((16 + Math.Sqrt(144 * N +` ` ` `256)) / 36);` ` ` ` ` `// Condition to check if the` ` ` `// N is a icosagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `public` `static` `void` `Main(` `string` `[] args)` `{` ` ` ` ` `// Given Number` ` ` `int` `N = 20;` ` ` `// Function call` ` ` `if` `(iicosagonal(N))` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by rutvik_56` |

## Javascript

`<script>` `// Javascript program for the above approach` `// Function to check if the number` `// N is a icosagonal number` `function` `iicosagonal(N)` `{` ` ` `var` `n` ` ` `= (16 + Math.sqrt(144 * N + 256))` ` ` `/ 36;` ` ` `// Condition to check if the` ` ` `// N is a icosagonal number` ` ` `return` `(n - parseInt(n)) == 0;` `}` `// Driver Code` `// Given Number` `var` `N = 20;` `// Function call` `if` `(iicosagonal(N)) {` ` ` `document.write( ` `"Yes"` `);` `}` `else` `{` ` ` `document.write(` `"No"` `);` `}` `</script>` |

**Output:**

Yes

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

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