Painting Eggs

5000ms

262144K

Description:

The Bitlandians are quite weird people. They have very peculiar customs.

As is customary, Uncle J. wants to have n eggs painted for Bitruz (an ancient Bitland festival). He has asked G. and A. to do the work.

The kids are excited because just as is customary, they're going to be paid for the job!

Overall uncle J. has got n eggs. G. named his price for painting each egg. Similarly, A. named his price for painting each egg. It turns out that for each egg the sum of the money both A. and G. want for the painting equals 1000.

Uncle J. wants to distribute the eggs between the children so as to give each egg to exactly one child. Also, Uncle J. wants the total money paid to A. to be different from the total money paid to G. by no more than 500.

Help Uncle J. Find the required distribution of eggs or otherwise say that distributing the eggs in the required manner is impossible.

Input:

The first line contains integer n (1 ≤ n ≤ 10⁶) — the number of eggs.

Next n lines contain two integers a_i and g_i each (0 ≤ a_i, g_i ≤ 1000; a_i + g_i = 1000): a_i is the price said by A. for the i-th egg and g_i is the price said by G. for the i-th egg.

Output:

If it is impossible to assign the painting, print "-1" (without quotes).

Otherwise print a string, consisting of n letters "G" and "A". The i-th letter of this string should represent the child who will get the i-th egg in the required distribution. Letter "A" represents A. and letter "G" represents G. If we denote the money Uncle J. must pay A. for the painting as S_a, and the money Uncle J. must pay G. for the painting as S_g, then this inequality must hold: |S_a - S_g| ≤ 500.

If there are several solutions, you are allowed to print any of them.

Sample Input:

2
1 999
999 1

Sample Output:

AG

Sample Input:

Sample Output:

AGA

Informação

Provedor Codeforces

Código CF282B