B. Painting Eggs

time limit per test

5 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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 test(s)

input

2 1 999 999 1

output

AG

input

3 400 600 400 600 400 600

output

AGA


#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>

using namespace std;

const int MAXN=1000005;

struct egg
{
	int a,g;
	int id;
	char ch;
}eggs[MAXN];
int n;

bool operator<(const egg a,const egg b)
{
	return a.a<b.a;
}

int cmp(const void *a,const void *b)
{
	return ((egg *)a)->id < ((egg *)b)->id;
}

int Abs(int a)
{
	if(a<0)return -a;
	return a;
}

int main()
{
	int ans1,ans2,ans;
	int st,ed;
	int tmp1,tmp2;
	while(cin>>n)
	{
		for(int i=0;i<n;i++)
		{
			cin>>eggs[i].a>>eggs[i].g;
			eggs[i].id=i;
		}
		sort(eggs,eggs+n);
		ans1=0;ans2=0;
		st=0;ed=n-1;
		while(st<=ed)
		{
			tmp1=Abs(ans1+eggs[st].a-ans2);
			tmp2=Abs(ans2+eggs[ed].g-ans1);
			if(tmp1<=Abs(ans2-ans1))
			{
				ans1+=eggs[st].a;
				eggs[st].ch='A';
				st++;
			}
			else if(tmp2<=Abs(ans2-ans1))
			{
				//if(ans2+eggs[ed].g)
				ans2+=eggs[ed].g;
				eggs[ed].ch='G';
				ed--;
			}
			else if(tmp1<=tmp2)
			{
				ans1+=eggs[st].a;
				eggs[st].ch='A';
				st++;
			}
			else
			{
				ans2+=eggs[ed].g;
				eggs[ed].ch='G';
				ed--;
			}
		}
		ans=ans1-ans2;
		if(ans<0)ans=-ans;
		if(ans>500)cout<<-1<<endl;
		else
		{
			qsort(eggs,n,sizeof(egg),cmp);
			for(int i=0;i<n;i++)
			  cout<<eggs[i].ch;
			cout<<endl;
		}
	}
	//system("pause");
	return 0;
}