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Time limit1sMemory limit512 MB

Summary

Build a strictly increasing length-N sequence with values at most 1000, second element 2, and last element prime.

Level: Easy3 of 10
Topics: Math, Number theory, Greedy, Implementation
Solved: No attempts yet

Problem

Given $N$ , find a sequence $A$ that satisfies the following conditions.

The length of $A$ is $N$ .
For $1 \le i \le N-1$ , $A_i < A_{i+1}$ must hold.
$1 \le A_i \le 1{,}000$ must hold.
$A_2$ must be $2$ .
$A_N$ must be a prime number.

Input

The first line gives $N$ .

Output

On the first line, print $N$ .

On the second line, print $A_1, A_2, \dots, A_N$ separated by spaces.

Constraints

$5 \le N \le 50$

Examples1

Example 1
Input
```
5
```
Expected output
```
5
1 2 8 10 37
```

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