Tautonym Puzzle

We will call a string x good if it satisfies the following condition:

• Condition: x can be represented as a concatenation of two copies of another string y of length at least 1.

For example, aa and bubobubo are good; an empty string, a, abcabcabc and abba are not good.

Eagle and Owl created a puzzle on good strings. Find one string s that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem.

• 1 ≤ |s| ≤ 200
• Each character of s is one of the 100 characters represented by the integers 1 through 100.
• Among the 2^{|s|} subsequences of s, exactly N are good strings.

Constraints

• 1 ≤ N ≤ 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

In the first line, print |s|, the length of s. In the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.

Examples

Input

7

Output

4 1 1 1 1

Input

299

Output

23 32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10

inputFormat

Input

Input is given from Standard Input in the following format:

N

outputFormat

Output

In the first line, print |s|, the length of s. In the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.

Examples

Input

7

Output

4 1 1 1 1

Input

299

Output

23 32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10

样例

7

4
1 1 1 1

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