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 PYTHON3):

Solution:
#!/usr/bin/env python
from __future__ import division, print_function
import math
import os
import sys
from sys import stdin,stdout
from io import BytesIO, IOBase
from itertools import accumulate
from collections import deque
#sys.setrecursionlimit(10**5)
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip
#sys.setrecursionlimit(10**6)

# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

input = lambda: sys.stdin.readline().rstrip("\r\n")
#-----------------------------------------------------------------

def regularbracket(t):
    p=0
    for i in t:
        if i=="(":
            p+=1
        else:
            p-=1
        if p<0:
            return False
    else:
        if p>0:
            return False
        else:
            return True

#-------------------------------------------------
def binarySearchCount(arr, n, key):
    left = 0
    right = n - 1

    count = 0

    while (left <= right):
        mid = int((right + left) / 2)

        # Check if middle element is
        # less than or equal to key
        if (arr[mid] <= key):
            count = mid+1
            left = mid + 1

        # If key is smaller, ignore right half
        else:
            right = mid - 1
    return count
#------------------------------reverse string(pallindrome)
def reverse1(string):
    pp=""
    for i in string[::-1]:
        pp+=i
    if pp==string:
        return True
    return False
#--------------------------------reverse list(paindrome)
def reverse2(list1):
    l=[]
    for i in list1[::-1]:
        l.append(i)
    if l==list1:
        return True
    return False
# endregion
import math
def mex(list1):
    #list1 = sorted(list1)
    p = max(list1)+1
    for i in range(len(list1)):
        if list1[i]!=i:
            p = i
            break
    return p
#----endregion
"""
d,hrs = map(int,input().split())
cnt=0
cnt2=0
cnt3=0
l=[]
a=[]
for _ in range(d):
    mint,maxt = map(int,input().split())
    cnt+=maxt
    cnt3+=mint
    l.append(maxt)
    a.append(mint)
if cnt<hrs or cnt3>hrs:
    print("NO")
else:
    print("YES")
    if cnt==hrs:
        for i in range(d):
            print(l[i],end=" ")
        print()
    else:
        for i in range(d):
            x = l[i]-a[i]
            j=1
            while(j<=x):
                if cnt3==hrs:
                    break
                cnt3+=1
                j+=1
                a[i]+=1
        for i in range(len(a)):
            print(a[i],end=" ")
        print()
"""
def main():
    n = int(input())
    aa =0
    gg =0
    for _ in range(n):
        a,g = map(int,input().split())
        if gg+a-aa<=500:
            gg+=a
            print("A",end="")
        else:
            aa+=g
            print("G",end="")
if __name__ == '__main__':
    main()