Taco Sequence Generation

You are given an integer N and your task is to generate a sequence S of length N defined as follows:

\(S_0 = 0,\; S_1 = 1\), and for all \(i \geq 2\):

\(S_i = S_{i-1} + S_{i-2} + i\)

For example:

• If N = 1, the sequence is: [0]
• If N = 3, the sequence is: [0, 1, 3]
• If N = 5, the sequence is: [0, 1, 3, 7, 14]

Your program should read the input from standard input (stdin) and output the sequence numbers separated by a space to standard output (stdout).

inputFormat

The input consists of a single integer N (N ≥ 1), representing the number of elements in the sequence to generate.

outputFormat

Output the generated sequence with each number separated by a single space.

## sample

1

0

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