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.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class CF282B {
    static BufferedReader __in;
    static PrintWriter __out;
    static StringTokenizer input;

    public static void main(String[] args) throws IOException {
        __in = new BufferedReader(new InputStreamReader(System.in));
        __out = new PrintWriter(new OutputStreamWriter(System.out));

        int n = ri(), a = 0, g = 0;
        StringBuilder sb = new StringBuilder();
        while(n --> 0) {
            int x = rni(), y = ni();
            if(a + x - g < 500) {
                a += x;
                sb.append("A");
            } else {
                g += y;
                sb.append("G");
            }
        }
        prln(sb);

        close();
    }

    // references
    // IBIG = 1e9 + 7
    // IRAND ~= 3e8
    // IMAX ~= 2e10
    // LMAX ~= 9e18
    // constants
    static final int IBIG = 1000000007;
    static final int IRAND = 327859546;
    static final int IMAX = 2147483647;
    static final int IMIN = -2147483648;
    static final long LMAX = 9223372036854775807L;
    static final long LMIN = -9223372036854775808L;
    // util
    static int minof(int a, int b, int c) {return min(a, min(b, c));}
    static int minof(int... x) {return x.length == 1 ? x[0] : x.length == 2 ? min(x[0], x[1]) : min(x[0], minstarting(1, x));}
    static int minstarting(int offset, int... x) {assert x.length > 2; return offset == x.length - 2 ? min(x[offset], x[offset + 1]) : min(x[offset], minstarting(offset + 1, x));}
    static long minof(long a, long b, long c) {return min(a, min(b, c));}
    static long minof(long... x) {return x.length == 1 ? x[0] : x.length == 2 ? min(x[0], x[1]) : min(x[0], minstarting(1, x));}
    static long minstarting(int offset, long... x) {assert x.length > 2; return offset == x.length - 2 ? min(x[offset], x[offset + 1]) : min(x[offset], minstarting(offset + 1, x));}
    static int maxof(int a, int b, int c) {return max(a, max(b, c));}
    static int maxof(int... x) {return x.length == 1 ? x[0] : x.length == 2 ? max(x[0], x[1]) : max(x[0], maxstarting(1, x));}
    static int maxstarting(int offset, int... x) {assert x.length > 2; return offset == x.length - 2 ? max(x[offset], x[offset + 1]) : max(x[offset], maxstarting(offset + 1, x));}
    static long maxof(long a, long b, long c) {return max(a, max(b, c));}
    static long maxof(long... x) {return x.length == 1 ? x[0] : x.length == 2 ? max(x[0], x[1]) : max(x[0], maxstarting(1, x));}
    static long maxstarting(int offset, long... x) {assert x.length > 2; return offset == x.length - 2 ? max(x[offset], x[offset + 1]) : max(x[offset], maxstarting(offset + 1, x));}
    static int powi(int a, int b) {if(a == 0) return 0; int ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static long powl(long a, int b) {if(a == 0) return 0; long ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static int floori(double d) {return (int)d;}
    static int ceili(double d) {return (int)ceil(d);}
    static long floorl(double d) {return (long)d;}
    static long ceill(double d) {return (long)ceil(d);}
    // input
    static void r() throws IOException {input = new StringTokenizer(__in.readLine());}
    static int ri() throws IOException {return Integer.parseInt(__in.readLine());}
    static long rl() throws IOException {return Long.parseLong(__in.readLine());}
    static int[] ria(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()); return a;}
    static long[] rla(int n) throws IOException {long[] a = new long[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Long.parseLong(input.nextToken()); return a;}
    static char[] rcha() throws IOException {return __in.readLine().toCharArray();}
    static String rline() throws IOException {return __in.readLine();}
    static int rni() throws IOException {input = new StringTokenizer(__in.readLine()); return Integer.parseInt(input.nextToken());}
    static int ni() {return Integer.parseInt(input.nextToken());}
    static long rnl() throws IOException {input = new StringTokenizer(__in.readLine()); return Long.parseLong(input.nextToken());}
    static long nl() {return Long.parseLong(input.nextToken());}
    // output
    static void pr(int i) {__out.print(i);}
    static void prln(int i) {__out.println(i);}
    static void pr(long l) {__out.print(l);}
    static void prln(long l) {__out.println(l);}
    static void pr(double d) {__out.print(d);}
    static void prln(double d) {__out.println(d);}
    static void pr(char c) {__out.print(c);}
    static void prln(char c) {__out.println(c);}
    static void pr(char[] s) {__out.print(new String(s));}
    static void prln(char[] s) {__out.println(new String(s));}
    static void pr(String s) {__out.print(s);}
    static void prln(String s) {__out.println(s);}
    static void pr(Object o) {__out.print(o);}
    static void prln(Object o) {__out.println(o);}
    static void prln() {__out.println();}
    static void pryes() {__out.println("yes");}
    static void pry() {__out.println("Yes");}
    static void prY() {__out.println("YES");}
    static void prno() {__out.println("no");}
    static void prn() {__out.println("No");}
    static void prN() {__out.println("NO");}
    static void pryesno(boolean b) {__out.println(b ? "yes" : "no");};
    static void pryn(boolean b) {__out.println(b ? "Yes" : "No");}
    static void prYN(boolean b) {__out.println(b ? "YES" : "NO");}
    static void prln(int... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
    static void prln(long... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
    static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for(int i = 0; i < n; __out.print(iter.next()), __out.print(' '), ++i); __out.println(iter.next());}
    static void flush() {__out.flush();}
    static void close() {__out.close();}}