CF282B.Painting Eggs

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.

Bitland 人是一群非常古怪的人，他们有着极为独特的习俗。

按照惯例，J 叔叔想为 Bitruz 节（Bitland 古老的节日）准备 $ n $ 个彩蛋。他请了 G. 和 A. 两个孩子来完成这项工作。

孩子们非常兴奋，因为按照惯例，他们将因此获得报酬！

J 叔叔一共有 $ n $ 个鸡蛋。G. 为每个鸡蛋的彩绘工作开出了自己的报价；同样地，A. 也为每个鸡蛋的彩绘工作开出了自己的报价。结果发现：对每个鸡蛋而言，A. 和 G. 所要求的报酬之和恰好为 1000。

J 叔叔希望将这些鸡蛋分配给两个孩子，使得每个鸡蛋恰好分给其中一个孩子。此外，J 叔叔还希望付给 A. 的总金额与付给 G. 的总金额之差的绝对值不超过 500。

请帮助 J 叔叔找出满足上述要求的鸡蛋分配方案；若不存在这样的分配方案，则说明其不可能实现。

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.

第一行包含一个整数 $n$（$1 \leq n \leq 10^6$）—— 鸡蛋的数量。

接下来的 $n$ 行，每行包含两个整数 $a_i$ 和 $g_i$（$0 \leq a_i, g_i \leq 1000$；且 $a_i + g_i = 1000$）：其中 $a_i$ 表示 A 对第 $i$ 个鸡蛋所报的价格，$g_i$ 表示 G 对第 $i$ 个鸡蛋所报的价格。

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.

如果无法分配画作，则输出 -1（不带引号）。

否则，输出一个由 n 个字母 "G" 和 "A" 组成的字符串。该字符串的第 i 个字母表示在所要求的分配方案中获得第 i 个鸡蛋的孩子："A" 表示孩子 A.，"G" 表示孩子 G.。设 Uncle J. 为画作需支付给 A. 的金额为 S__a，支付给 G. 的金额为 S__g，则必须满足如下不等式：|S__a − S__g| ≤ 500。

若存在多个解，输出任意一个即可。