# Find the good permutation of first N natural numbers

Given an integer **N**, the task is to print a good permutation of first **N** natural numbers. Let’s denote the **i ^{th}** element of the permutation be

**p**.

_{i}A good permutation is a permutation such that for all

**1 ≤ i ≤ N**the following equations hold true,

**p**_{pi}= i**p**_{i}!= i

Basically above expressions mean, no value is equal to its position.

If no such good permutation exists then print **-1**.

**Examples:**

Input:N = 1

Output:-1

No good permutation exists.

Input:N = 2

Output:2 1

Position of 2 is 1 and position of 1 is 2.

**Approach:** Consider permutation **p** such that **p _{i} = i**. Actually,

**p**is a sequence of numbers from

**1**to

**N**and

**p**.

_{pi}= iNow the only trick is to change the permutation to satisfy the second equation i.e.

**p**. Let’s swap every two consecutive elements. More formally, for each

_{i}!= i**k**:

**2k ≤ n**let's swap

**p**and

_{2k – 1}**p**. It’s easy to see that the obtained permutation satisfies both the equations for every

_{2k}**n**with the only exception: when n is odd, there is no answer and we should print

**-1**.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to print the good permutation ` `// of first N natural numbers ` `int` `printPermutation(` `int` `n) ` `{ ` ` ` `// If n is odd ` ` ` `if` `(n % 2 != 0) ` ` ` `cout << -1; ` ` ` ` ` `// Otherwise ` ` ` `else` ` ` `for` `(` `int` `i = 1; i <= n / 2; i++) ` ` ` `cout << 2 * i << ` `" "` `<< 2 * i - 1 << ` `" "` `; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n = 4; ` ` ` `printPermutation(n); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java implementation of the approach ` ` ` `class` `GFG ` `{ ` ` ` `// Function to print the good permutation ` `// of first N natural numbers ` `static` `int` `printPermutation(` `int` `n) ` `{ ` ` ` `// If n is odd ` ` ` `if` `(n % ` `2` `!= ` `0` `) ` ` ` `{ ` ` ` `System.out.println(` `"-1"` `); ` ` ` `} ` ` ` ` ` `// Otherwise ` ` ` `else` ` ` `for` `(` `int` `i = ` `1` `; i <= n / ` `2` `; i++) ` ` ` `{ ` ` ` `System.out.print(` `2` `* i + ` `" "` `+ ((` `2` `* i) - ` `1` `) + ` `" "` `); ` ` ` `} ` ` ` ` ` `return` `n; ` ` ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String []args) ` `{ ` ` ` `int` `n = ` `4` `; ` ` ` `printPermutation(n); ` `} ` `} ` ` ` `// This code contributed by Rajput-Ji ` |

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## Python3

`# Python3 implementation of the approach ` ` ` `# Function to print the good permutation ` `# of first N natural numbers ` `def` `printPermutation(n): ` ` ` ` ` `# If n is odd ` ` ` `if` `(n ` `%` `2` `!` `=` `0` `): ` ` ` `print` `(` `-` `1` `); ` ` ` ` ` `# Otherwise ` ` ` `else` `: ` ` ` `for` `i ` `in` `range` `(` `1` `, (n ` `/` `/` `2` `) ` `+` `1` `): ` ` ` `print` `((` `2` `*` `i), (` `2` `*` `i ` `-` `1` `), end ` `=` `" "` `); ` ` ` `# Driver code ` `n ` `=` `4` `; ` `printPermutation(n); ` ` ` `# This code is contributed by mits ` |

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## C#

`// C# implementation of the approach ` `using` `System; ` ` ` `class` `GFG { ` ` ` `// Function to print the good permutation ` `// of first N natural numbers ` `static` `int` `printPermutation(` `int` `n) ` `{ ` ` ` `// If n is odd ` ` ` `if` `(n % 2 != 0) ` ` ` `{ ` ` ` `Console.WriteLine(` `"-1"` `); ` ` ` `} ` ` ` ` ` `// Otherwise ` ` ` `else` ` ` `for` `(` `int` `i = 1; i <= n / 2; i++) ` ` ` `{ ` ` ` `Console.WriteLine(2 * i + ` `" "` `+ ((2 * i) - 1) + ` `" "` `); ` ` ` `} ` ` ` ` ` `return` `n; ` ` ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main(String []args) ` `{ ` ` ` `int` `n = 4; ` ` ` `printPermutation(n); ` `} ` `} ` ` ` `// This code is contributed by Kirti_Mangal ` |

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## PHP

`<?phP ` `// PHP implementation of the approach ` ` ` `// Function to print the good permutation ` `// of first N natural numbers ` `function` `printPermutation(` `$n` `) ` `{ ` ` ` `// If n is odd ` ` ` `if` `(` `$n` `% 2 != 0) ` ` ` `{ ` ` ` `echo` `(` `"-1"` `); ` ` ` `} ` ` ` ` ` `// Otherwise ` ` ` `else` ` ` `for` `(` `$i` `= 1; ` `$i` `<= ` `$n` `/ 2; ` `$i` `++) ` ` ` `{ ` ` ` `echo` `(2 * ` `$i` `. ` `" "` `. ` ` ` `((2 * ` `$i` `) - 1) . ` `" "` `); ` ` ` `} ` ` ` ` ` `return` `$n` `; ` `} ` ` ` `// Driver code ` `$n` `= 4; ` `printPermutation(` `$n` `); ` ` ` `// This code contributed ` `// by Code_Mech. ` `?> ` |

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**Output:**

2 1 4 3

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