Fair Division Of Coins

You have n gold coins with you. You wish to divide them among three of your friends under the following conditions:

• all three of them should get a non-zero share
• no two of them should get the same number of coins
• you should not have any coins left with you at the end of the sharing process

Input

Four lines. The first line is the number of coins you have. The next three lines are the shares given to your three friends. All inputs are non-negative integers.

Output

A single line: FAIR if the division satisfies all three conditions, UNFAIR otherwise.

Example

Input:

10
2
3
5

Output:

FAIR

Your task

Write a complete program: read the input with input() and print the result with print().

Example

Input

10
2
3
5

Output

FAIR