Erase Securely#6255

Erase Securely

1 second
128 megabytes
Very easy

Jon Marius is the computer expert at his company and has now been tasked with finding some software for erasing data properly. It is very important that the data should not be recoverable afterwards, so it should be overwritten on the hard drive several times. Unable to find any free program up to the task, Jon Marius decides to write such a program himself. The user interface is simple: it only asks for the file to be destroyed and , the number of times it should be overwritten. This number can range from (quick deletion) to (maximum security). Jon Marius processes the file bit by bit and does not consider writing a zero where there was already a zero as really overwriting. So for each of the sweeps, he overwrites each zero with a one and each one with a zero.

Jon Marius knows that independent testing is important, so he has asked you to write the verification routine. He will not listen to your objections to the algorithm so eventually you give in.

Input

The first line contains a single integer (1 \leq n \leq 20).

The two following lines each contain a string containing only the characters and . The first of these lines represents the bits of the file before deletion and the second the bits at the same position on the hard drive after the file has been deleted.

The lengths of these strings are equal and between and characters.

Output

Output a single line containing either the words Deletion succeeded if each bit is switched times, or Deletion failed if this is not the case.

Examples

Example 1

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Example 2

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