The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Unknown Language Round 2 |
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Finished |

The following languages are only available languages for the problems from the contest

Unknown Language Round 2:

- Io-2008-01-07 (Win32)

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I. Goofy Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

stdinoutput

stdoutThe non-negative integer *a* is a divisor of the non-negative integer *b* if and only if there exists a positive integer *c* such that *a* × *c* = *b*.

Some numbers are really interesting. Commander Surena defines some interesting properties for non-negative integers:

- An integer is happy if it is divisible by at least one of its digits and not by all of them.
- An integer is happier if it is divisible by all of its digits.
- An integer is upset if it's divisible by none of its digits.

Surena asks you to find out if a given number is happy, happier or upset.

Input

Input contains a single non-negative integer *n* (1 ≤ *n* ≤ 10^{8}).

Output

Write on a single line the type of the integer: happy, happier or upset. Print the type in lowercase letters.

Examples

Input

99

Output

happier

Input

29994

Output

happy

Input

23

Output

upset

Note

In the second test 29994 is only divisible by 2.

In the third test 23 is a prime number.

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