Problem Description

There is a new type of stack computer where the memory is an initially empty sequence. The computer supports three operations:
- $\tt 1$ - Append the integer $1$ to the end of the sequence. This operation can be performed at any time.
- $\tt$ - Duplicate the last number in the sequence and append it to the end. This operation can only be performed when the sequence is not empty.
- $\tt$ - Remove (and delete) the last two numbers from the sequence, add them together, and append the result to the end of the sequence. This operation can only be performed when there are at least two numbers in the sequence.

Given a positive integer, you need to output a program (sequence of operations) of length no more than $200$ that, when executed, results in a sequence of exactly one number, which is exactly $n$. The figure below shows a program that results in $8$.

Input Format

Input consists of a single line containing a positive integer $n$, representing the desired output number.

Output Format

Output a program consisting of several lines (no more than $200$ lines, otherwise it will be considered incorrect) that meets the above requirements. If there are multiple solutions, output any one of them. Note that $\tt$ and $\tt$ should be in lowercase.

Sample Input and Output

Sample Input #1

1

Sample Output #1

1

Sample Input #2

8

Sample Output #2

1
1
add
dup
add
dup
add

Notes

For $60\%$ of the test cases, $1 \le n \le 10^4$.

For $100\%$ of the test cases, $1 \le n \le 10^9$.

This problem originally had a full score of $15\text{pts}$.

见题面 Input 部分

见题面 Output 部分