Problem: 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 ai and gi each (0 ≤ ai, gi ≤ 1000; ai + gi = 1000): ai is the price said by A. for the i-th egg and gi 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 Sa, and the money Uncle J. must pay G. for the painting as Sg, then this inequality must hold: |Sa - Sg| ≤ 500. 

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

Examples

Input

2
1 999
999 1


Output

AG


Input

3
400 600
400 600
400 600


Output

AGA

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

//import graph_representation.edge;
public class hacker49 {
	public static int r1=0;
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
static 	ArrayList<Integer>[] f=new ArrayList[200001];

	static HashMap<Long,Integer> e=new HashMap<>();
	public static void main(String[] args) {
		OutputStream outputStream =System.out;
	    PrintWriter out =new PrintWriter(outputStream);
		FastReader s=new FastReader();
double n=s.nextDouble();
double sum=0;
for(double i=1;i<=n;i++) {
	double x1=s.nextDouble();
	double x2=s.nextDouble();
	sum+=x1;
}
long l=(long) Math.floor((n-((sum-500)/1000)));
long r=(long) Math.ceil((n-((sum+500)/1000)));
//System.out.println(r+" "+l);
if(r>l) {
	out.println(-1);
}else {
	for(int i=0;i<r;i++) {
		out.print('A');
	}
	for(int i=0;i<(int)(n-r);i++) {
		out.print('G');
	}
}

out.close();
		
	}
//	static int[] vis=new int[200001];
	static void dfs(int node) {
		vis[node]=1;
		for(int i=0;i<f[node].size();i++) {
			if(vis[f[node].get(i)]==0 && f[node].get(i)!=node) {
				dfs(f[node].get(i));
			}
		}
	}
	static int LongestPalindromicPrefix(String str)
	{
	  
	    // Create temporary String
	    String temp = str + '?';
	  
	    // Reverse the String str
	    str = reverse(str);
	  
	    // Append String str to temp
	    temp += str;
	  
	    // Find the length of String temp
	    int n = temp.length();
	  
	    // lps[] array for String temp
	    int []lps = new int[n];
	  
	    // Intialise every value with zero
	    Arrays.fill(lps, 0);
	  
	    // Iterate the String temp
	    for(int i = 1; i < n; i++)
	    {
	          
	       // Length of longest prefix
	       // till less than i
	       int len = lps[i - 1];
	         
	       // Calculate length for i+1
	       while (len > 0 && temp.charAt(len) != 
	                         temp.charAt(i)) 
	       {
	           len = lps[len - 1];
	       }
	         
	       // If character at current index
	       // len are same then increament
	       // length by 1
	       if (temp.charAt(i) == temp.charAt(len))
	       {
	           len++;
	       }
	         
	       // Update the length at current
	       // index to len
	       lps[i] = len;
	    }
	  
	    // Print the palindromic String 
	    // of max_len
//	    System.out.print(temp.substring(0, lps[n - 1]));
	return lps[n-1];
	}
	  
	static String reverse(String input)
	{
	    char[] a = input.toCharArray();
	    int l, r = a.length - 1;
	      
	    for(l = 0; l < r; l++, r--)
	    {
	       char temp = a[l];
	       a[l] = a[r];
	       a[r] = temp;
	    }
	    return String.valueOf(a);
	}
	public static void lps(String str,TreeSet<Integer>[] f,int n,TreeSet<Integer>[] f2) {
		boolean[][] dp=new boolean[n][n];
		for(int g=0;g<n;g++) {
			for(int i=0,j=g;j<n;i++,j++) {
				if(g==0) {
					dp[i][j]=true;
				}else if(g==1) {
					if(str.charAt(i)==str.charAt(j)) {
						dp[i][j]=true;
					}else {
						dp[i][j]=false;
					}
				}else {
					if(str.charAt(i)==str.charAt(j) && dp[i+1][j-1]) {
						dp[i][j]=true;
					}else {
						dp[i][j]=false;
					}
				}
				if(dp[i][j]) {
					f[i].add(j);
					f2[n-j-1].add(n-i-1);
				}
			}
		}
			
	}
	static int[] vis=new int[200001];
	
static int[] is_prime=new int[1001];
static ArrayList<Integer>[] y=new ArrayList[100001];
	public static ArrayList<Integer> primes=new ArrayList<>();
 	public static void sieve() {
		long maxN=1000;
		for(int i=1;i<=maxN;i++) {
			is_prime[i]=1;
		}
		is_prime[0]=0;
		is_prime[1]=0;
		for(long i=2;i*i<=maxN;i++) {
			if(is_prime[(int) i]==1) {
//				primes.add((int) i);
				for(long j=i*i;j<=maxN;j+=i) {
					is_prime[(int) j]=0;
				}
			}
		}
//		for(int i=1;i<=1000000;i++) {
//			pre[i]=pre[i-1]+is_prime[i];
//		}
		for(int i=0;i<=maxN;i++) {
			if(is_prime[i]==1) {
				primes.add(i);
			}
		}
//		int count=0;
//		for(long i=1;i<=maxN;i++) {
//			if(is_prime[(int) i]==1) {
//				count++;
//			}
//			if(is_prime[count]==1) {
//				arr[(int) i]=1;
//			}else {
//				arr[(int)i]=0;
//			}
//		}
	}
 	
 	static boolean isgood(long k) {
 		boolean p=true;
 		out:while(k>1) {
 			while(k%3==0 && k>1) {
 				k/=3;
 			}
 			if(k==1) {
 				break out;
 			}
 			k-=1;
 			if(k%3!=0) {
 				p=false;
 				break out;
 			}
 		}
 		return p;
 		
 	}
	static int[] r=new int[100001];
	static class pair5{
		private int a;
		private int b;
		pair5(int a,int b){
			this.a=a;
			this.b=b;
		}
	}
	static ArrayList<Integer> o=new ArrayList<>();
	static void bfs(int node) {
		PriorityQueue<Integer> q=new PriorityQueue<>();
		q.add(1);
//	o.add(1);
	vis[1]=1;
    while(!q.isEmpty()) {
    	int g=q.poll();
//    	vis[g]=1;
    	o.add(g);
    	for(int i=0;i<y[g].size();i++) {
    		if(vis[y[g].get(i)]==0) {
    			q.add(y[g].get(i));
    			vis[y[g].get(i)]=1;
    		}
    	}
    }
		
	}
	static int[] dx= {0,-1,0,1};
	static int[] dy= {1,0,-1,0};
	static boolean is(int x,int y,int n,int m) {
		if(x<=n && x>=1 && y<=m && y>=1) {
			return true;
			
		}
		return false;
	}
//	static ArrayList<pair5>[] t=new ArrayList[51];
	
	static class pair implements Comparable<pair>{
		private long i;
		private long v;
		pair(long i,long v){
			this.i=i;
			this.v=v;
		}
		public int compareTo(pair o) {
//			if(o.v<this.v) {
//				return -1;
//			}else {
//				return 1;
//			}
			return Long.compare(this.v, o.v);
		}
		
	}
	static class pair2 implements Comparable<pair2>{
		private long a;
		private long b;
		pair2(long a,long b){
			this.a=a;
			this.b=b;
		}
		public int compareTo(pair2 o) {
//			if(o.v<this.v) {
//				return -1;
//			}else {
//				return 1;
//			}
			return Long.compare(this.a, o.a);
		}
		
	}
	
	static int nextPowerOf2(int n) 
	{ 
	    n--; 
	    n |= n >> 1; 
	    n |= n >> 2; 
	    n |= n >> 4; 
	    n |= n >> 8; 
	    n |= n >> 16; 
	    n++; 
	      
	    return n; 
	} 
//	static class node{
//		private int a;
//		private int b;
//		private int c;
//		private int d;
//		
//	}
	
	
	public static class node{
		private int a;
		private int b;
		node(int a,int b){
			this.a=a;
			this.b=b;
		}
	}

	public static long GCD(long a,long b) {
		if(b==(long)0) {
			return a;
		}
		return GCD(b , a%b);
	}
//	public static void Create(node[] arr,node[] segtree,int low,int high,int pos) {
//		if(low==high) {
//			segtree[pos]=arr[low];
//			return;
//		}
//		int mid=(low+high)/2;
//		Create(arr,segtree,low,mid,2*pos+1);
//		Create(arr,segtree,mid+1,high,2*pos+2);
//		if(segtree[2*pos+1].a+segtree[2*pos+2].a>=10) {
//			int a=segtree[2*pos+1].a;
//			int b=segtree[2*pos+2].a;
//			int c=segtree[2*pos+1].b;
//			int d=segtree[2*pos+2].b;
//			segtree[pos]=new node((a+b)%10,1+c+d);
//		}else {
//			int a=segtree[2*pos+1].a;
//			int b=segtree[2*pos+2].a;
//			int c=segtree[2*pos+1].b;
//			int d=segtree[2*pos+2].b;
//			segtree[pos]=new node(a+b,c+d);
//			
//		}
//	}
//	public static node Query(node[] segtree,int qlow,int qhigh,int low,int high,int pos) {
//		if(low>=qlow && high<=qhigh) {
//			return segtree[pos];
//		}
//		if(qhigh<low || qlow>high) {
//			return new node(0,0);
//		}
//		int mid=(low+high)/2;
//	 node a=Query(segtree,qlow,qhigh,low,mid,2*pos+1);
//	node b=Query(segtree,qlow,qhigh,mid+1,high,2*pos+2);
//	int c=a.a;
//	int d=b.a;
//	if(c+d>=10) {
//	node e=new node((c+d)%10,1+a.b+b.b);
//	return e;
//	}else {
//		node e=new node(c+d,a.b+b.b);
//		return e;
//	}
//	}
//	
	static class pair1 implements Comparable<pair1>{
		private int a;
		private int b;
		private int c;
		private int d;
		pair1(int a,int b,int c,int d){
			this.a=a;
			this.b=b;
			this.c=c;
			this.d=d;
		}
		public int compareTo(pair1 o) {
			if(this.a<o.a) {
				return 1;
			}else if(this.a==o.a) {
				if(this.b<o.b) {
					return 1;
				}else {
					return -1;
				}
			}else {
				return -1;
			}
				
		}
	}
	public static void update(long[] segtree,int low,int high,int qlow,int qhigh,long val,int pos) {
		if(qlow>high || qhigh<low) {
			return ;
		}
		if(low>=qlow &&qhigh>=high) {
			segtree[pos]+=val;
			return;
		}
		int mid=(low+high)/2;
		update(segtree,low,mid,qlow,qhigh,val,2*pos);
		update(segtree,mid+1,high,qlow,qhigh,val,2*pos+1);
		
	}
	public static long query(long[] segtree,int low,int high,int index,int pos) {
		
		if(low==high) {
			return segtree[pos];
		}
		int mid=(low+high)/2;
		long res=0;
		if(index<=mid) {
			res= query(segtree,low,mid,index,2*pos);
		}else {
			res=query(segtree,mid+1,high,index,2*pos+1);
		}
		return res+segtree[pos];
	}
	
//	public static class pair5{
//		private int a;
//		private int b;
//		pair5(int a,int b){
//			this.a=a;
//			this.b=b;
//		}
//		public int compareTo(pair5 o) {
//			return Integer.compare(o.b, this.b);
//		}
//	}
//	public static pair5[] merge_sort(pair5[] A, int start, int end) {
//		if (end > start) {
//			int mid = (end + start) / 2;
//			pair5[] v = merge_sort(A, start, mid);
//			pair5[] o = merge_sort(A, mid + 1, end);
//			return (merge(v, o));
//		} else {
//			pair5[] y = new pair5[1];
//			y[0] = A[start];
//			return y;
//		}
//	}
//	public static pair5[] merge(pair5 a[], pair5 b[]) {
////		int count=0;
//		pair5[] temp = new pair5[a.length + b.length];
//		int m = a.length;
//		int n = b.length;
//		int i = 0;
//		int j = 0;
//		int c = 0;
//		while (i < m && j < n) {
//			if (a[i].a < b[j].a) {
//				temp[c++] = a[i++];
//			} else {
//				temp[c++] = b[j++];
//			}
//		}
//		while (i < m) {
//			temp[c++] = a[i++];
//		}
//		while (j < n) {
//			temp[c++] = b[j++];
//		}
//		return temp;
//	}
////	
	public static int upper_bound(int[] a ,int n,int x) {
		int l=-1;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid]<x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return r;
				
	}

//	
//	
	public static long lower_bound(long n,long i) {
		long l=0;
		long r=n+1;
		while(r>l+1) {
			long mid=(l+r)/2;
//			System.out.println(mid);
//			mid*=mid;
			long y=2*mid-1;
			long r1=(y*y);
			if((r1-1)/2<i) {
				l=mid;
			}else {
				r=mid;
			}
//			System.out.println(l);
//			if(a[mid].i<x) {
//				l=mid;
//			}else {
//				r=mid;
//			}
		}
		return l;
				
	}
	public static int ty(int[] a, int x, int y)
    {
        Arrays.sort(a);
        int count=0;
        int n=a.length;
        for(int i=0;i<n;i++) {
        	int g=0;
        	if(x%a[i]==0) {
        		g=x/a[i];
        	}else {
        		g=x/a[i]+1;
        	}
        	int k1=upper_bound(a,n,g);
        	if(k1==n) {
        		count+=0;
        	}else {
        		int g1=0;
            	if(y%a[i]==0) {
            		g1=y/a[i];
            	}else {
            		g1=y/a[i]+1;
            	}
//            	int k2=lower_bound(a,n,g1);
//            	if(k2>=k1) {
//            		count+=(k2-k1+1);
//            	}
        	}
//        System.out.println(count);
        }
        return count;
        
    }
	static boolean isValid(int x,int y,int n,int m) {
		if(x>=1 && x<=n && y>=1 && y<=m) {
			return true;
		}else {
			return false;
		}
	}
	
	static long[] fac=new long[1000001];
	static void fac() {
		fac[0]=1;
		for(int i=1;i<=1000000;i++) {
//			fac[i]=((fac[i-1]%mod)*(i%mod))%mod;
		}
	}

	public static void init(int n) {
		
		for(int j=1;j<=n;j++) {
		for (int l=1; l<=Math.sqrt(j); l++)
        {
            if (j%l==0)
            {
                // If divisors are equal, print only one
                if (j/l == l) {
                    f[j].add(l);}
      
                else { // Otherwise print both
//                    System.out.print(i+" " + n/i + " " );
            f[j].add(l);
            f[j].add(j/l);
                }
                
            }
        }
		
		}
		
	}
	
	public static long[] merge_sort(long[] A, int start, int end) {
		if (end > start) {
			int mid = (end + start) / 2;
			long[] v = merge_sort(A, start, mid);
			long[] o = merge_sort(A, mid + 1, end);
			return (merge(v, o));
		} else {
			long[] y = new long[1];
			y[0] = A[start];
			return y;
		}
	}
	public static long[] merge(long a[], long b[]) {
//		int count=0;
		long[] temp = new long[a.length + b.length];
		int m = a.length;
		int n = b.length;
		int i = 0;
		int j = 0;
		int c = 0;
		while (i < m && j < n) {
			if (a[i] > b[j]) {
				temp[c++] = a[i++];
			
			} else {
				temp[c++] = b[j++];
			}
		}
		while (i < m) {
			temp[c++] = a[i++];
		}
		while (j < n) {
			temp[c++] = b[j++];
		}
		return temp;
	}
	
	public static int[] merge_sort1(int[] A, int start, int end) {
		if (end > start) {
			int mid = (end + start) / 2;
			int[] v = merge_sort1(A, start, mid);
			int[] o = merge_sort1(A, mid + 1, end);
			return (merge1(v, o));
		} else {
			int[] y = new int[1];
			y[0] = A[start];
			return y;
		}
	}
	public static int[] merge1(int a[], int b[]) {
//		int count=0;
		int[] temp = new int[a.length + b.length];
		int m = a.length;
		int n = b.length;
		int i = 0;
		int j = 0;
		int c = 0;
		while (i < m && j < n) {
			if (a[i] < b[j]) {
				temp[c++] = a[i++];
			
			} else {
				temp[c++] = b[j++];
			}
		}
		while (i < m) {
			temp[c++] = a[i++];
		}
		while (j < n) {
			temp[c++] = b[j++];
		}
		return temp;
	}
	
	static long MOD=1000000007;
	




//	for(int i=2;i<=100000;i++) {
		
	
}