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

Centered Dodecagonal Numberrepresents a dot in the center and other dots surrounding it in successive Dodecagonal Number(12 sided polygon) layers. The first few Centered Dodecagonal Numbers are1, 13, 37, 73 …

**Examples:**

Input:N = 13

Output:Yes

Explanation:

Second Centered dodecagonal number is 13.

Input:N = 30

Output:No

**Approach:**

- The
**K**term of the Centered Dodecagonal Number is given as:^{th} - As we have to check that the given number can be expressed as a Centered Dodecagonal Number or not. This can be checked as:

=>

=> - If the value of
**K**calculated using the above formula is an integer, then**N**is a Centered Dodecagonal Number. - Else the number
**N**is not a Centered Dodecagonal 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 Centered dodecagonal number ` `bool` `isCentereddodecagonal(` `int` `N) ` `{ ` ` ` `float` `n ` ` ` `= (6 + ` `sqrt` `(24 * N + 12)) ` ` ` `/ 12; ` ` ` ` ` `// Condition to check if N ` ` ` `// is a Centered Dodecagonal Number ` ` ` `return` `(n - (` `int` `)n) == 0; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `// Given Number ` ` ` `int` `N = 13; ` ` ` ` ` `// Function call ` ` ` `if` `(isCentereddodecagonal(N)) { ` ` ` `cout << ` `"Yes"` `; ` ` ` `} ` ` ` `else` `{ ` ` ` `cout << ` `"No"` `; ` ` ` `} ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program for the above approach ` `import` `java.util.*; ` ` ` `class` `GFG{ ` ` ` `// Function to check if number N ` `// is a centered dodecagonal number ` `static` `boolean` `isCentereddodecagonal(` `int` `N) ` `{ ` ` ` `float` `n = (` `float` `) ((` `6` `+ Math.sqrt(` `24` `* N + ` ` ` `12` `)) / ` `12` `); ` ` ` ` ` `// Condition to check if N is a ` ` ` `// centered dodecagonal number ` ` ` `return` `(n - (` `int` `)n) == ` `0` `; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` ` ` `// Given Number ` ` ` `int` `N = ` `13` `; ` ` ` ` ` `// Function call ` ` ` `if` `(isCentereddodecagonal(N)) ` ` ` `{ ` ` ` `System.out.print(` `"Yes"` `); ` ` ` `} ` ` ` `else` ` ` `{ ` ` ` `System.out.print(` `"No"` `); ` ` ` `} ` `} ` `} ` ` ` `// This code is contributed by sapnasingh4991 ` |

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## Python3

`# Python3 program for the above approach ` `import` `numpy as np ` ` ` `# Function to check if the number N ` `# is a centered dodecagonal number ` `def` `isCentereddodecagonal(N): ` ` ` ` ` `n ` `=` `(` `6` `+` `np.sqrt(` `24` `*` `N ` `+` `12` `)) ` `/` `12` ` ` ` ` `# Condition to check if N ` ` ` `# is a centered dodecagonal number ` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` ` ` `# Driver Code ` `N ` `=` `13` ` ` `# Function call ` `if` `(isCentereddodecagonal(N)): ` ` ` `print` `(` `"Yes"` `) ` `else` `: ` ` ` `print` `(` `"No"` `) ` ` ` `# This code is contributed by PratikBasu ` |

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## C#

`// C# program for the above approach ` `using` `System; ` ` ` `class` `GFG{ ` ` ` `// Function to check if number N ` `// is a centered dodecagonal number ` `static` `bool` `isCentereddodecagonal(` `int` `N) ` `{ ` ` ` `float` `n = (` `float` `) ((6 + Math.Sqrt(24 * N + ` ` ` `12)) / 12); ` ` ` ` ` `// Condition to check if N is a ` ` ` `// centered dodecagonal number ` ` ` `return` `(n - (` `int` `)n) == 0; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main(` `string` `[] args) ` `{ ` ` ` ` ` `// Given Number ` ` ` `int` `N = 13; ` ` ` ` ` `// Function call ` ` ` `if` `(isCentereddodecagonal(N)) ` ` ` `{ ` ` ` `Console.Write(` `"Yes"` `); ` ` ` `} ` ` ` `else` ` ` `{ ` ` ` `Console.Write(` `"No"` `); ` ` ` `} ` `} ` `} ` ` ` `// This code is contributed by rutvik_56 ` |

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**Output:**

Yes

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