Generate Special Sequence

Given a non-negative integer n, your task is to generate a sequence of n distinct positive integers S = [S₀, S₁, ..., S_n-1] that satisfies the following conditions:

• The sequence must start with 1, i.e. S₀ = 1.
• The sequence is strictly increasing: S₀ < S₁ < ... < S_n-1.
• For any two elements S_i and S_j with i < j, if the difference is \(k = S_j - S_i\) (where \(k > 1\)), then there must be at least \(k-1\) elements between them in the sequence. In other words, if the element S_j is added as the \(m^{th}\) number (i.e. at index m where m = j), then it must hold that:
  
  \[ S_j - S_i \geq (j - i) + 1 \] for all 0 ≤ i < j < n.

For example:

• For n = 1, the sequence is [1].
• For n = 3, the sequence is [1, 2, 4].
• For n = 5, the sequence is [1, 2, 4, 5, 7].
• For n = 10, the sequence is [1, 2, 4, 5, 7, 8, 10, 11, 13, 14].
• For n = 0, the sequence is empty.

Your program should read the input from standard input (stdin) and output the generated sequence to standard output (stdout) as space-separated integers on a single line. If the sequence is empty, output an empty line.

inputFormat

The input consists of a single integer n (0 ≤ n ≤ 1000), which denotes the length of the sequence to generate.

outputFormat

Output the generated sequence as space-separated integers on one line. If n is 0, output an empty line.

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