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, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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Unknown Language Round #3:

- Pike 7.8

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B. Friendly Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputKiana thinks two integers are friends if and only if one of them divides the other one. For example, 12 and 4 are friends, also 6 and 6 are friends too, but 120 and 36 are not.

A group of non-zero integers is called friendly, if each pair of its integers form a friend pair.

You are given a group of non-zero integers. See if they're friendly.

Input

The first line contains *n* (1 ≤ *n* ≤ 1000), where *n* — the number of integers in the group.

The next line contains the elements, sorted in the non-decreasing order. The numbers are comma separated, they have at most 7 digits in their decimal notation and do not have any leading zeros.

Output

If the group is friendly write "FRIENDS", else write "NOT FRIENDS".

Examples

Input

4

1,3,6,12

Output

FRIENDS

Input

3

1,2,9

Output

NOT FRIENDS

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