Codeforces Round 173 (Div. 2)
A. Bit++
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The classic programming language of Bitland is Bit++. This language is so peculiar and complicated.

The language is that peculiar as it has exactly one variable, called x. Also, there are two operations:

  • Operation ++ increases the value of variable x by 1.
  • Operation -- decreases the value of variable x by 1.

A statement in language Bit++ is a sequence, consisting of exactly one operation and one variable x. The statement is written without spaces, that is, it can only contain characters "+", "-", "X". Executing a statement means applying the operation it contains.

A programme in Bit++ is a sequence of statements, each of them needs to be executed. Executing a programme means executing all the statements it contains.

You're given a programme in language Bit++. The initial value of x is 0. Execute the programme and find its final value (the value of the variable when this programme is executed).

Input

The first line contains a single integer n (1 ≤ n ≤ 150) — the number of statements in the programme.

Next n lines contain a statement each. Each statement contains exactly one operation (++ or --) and exactly one variable x (denoted as letter «X»). Thus, there are no empty statements. The operation and the variable can be written in any order.

Output

Print a single integer — the final value of x.

Examples
Input
1
++X
Output
1
Input
2
X++
--X
Output
0
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 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
C. XOR and OR
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The Bitlandians are quite weird people. They do everything differently. They have a different alphabet so they have a different definition for a string.

A Bitlandish string is a string made only of characters "0" and "1".

BitHaval (the mayor of Bitland) loves to play with Bitlandish strings. He takes some Bitlandish string a, and applies several (possibly zero) operations to it. In one operation the mayor may take any two adjacent characters of a string, define one of them as x and the other one as y. Then he calculates two values p and q: p = x xor y, q = x or y. Then he replaces one of the two taken characters by p and the other one by q.

The xor operation means the bitwise excluding OR operation. The or operation is the bitwise OR operation.

So for example one operation can transform string 11 to string 10 or to string 01. String 1 cannot be transformed into any other string.

You've got two Bitlandish strings a and b. Your task is to check if it is possible for BitHaval to transform string a to string b in several (possibly zero) described operations.

Input

The first line contains Bitlandish string a, the second line contains Bitlandish string b. The strings can have different lengths.

It is guaranteed that the given strings only consist of characters "0" and "1". The strings are not empty, their length doesn't exceed 106.

Output

Print "YES" if a can be transformed into b, otherwise print "NO". Please do not print the quotes.

Examples
Input
11
10
Output
YES
Input
1
01
Output
NO
Input
000
101
Output
NO
D. Yet Another Number Game
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Since most contestants do not read this part, I have to repeat that Bitlandians are quite weird. They have their own jobs, their own working method, their own lives, their own sausages and their own games!

Since you are so curious about Bitland, I'll give you the chance of peeking at one of these games.

BitLGM and BitAryo are playing yet another of their crazy-looking genius-needed Bitlandish games. They've got a sequence of n non-negative integers a1, a2, ..., an. The players make moves in turns. BitLGM moves first. Each player can and must do one of the two following actions in his turn:

  • Take one of the integers (we'll denote it as ai). Choose integer x (1 ≤ x ≤ ai). And then decrease ai by x, that is, apply assignment: ai = ai - x.
  • Choose integer x . And then decrease all ai by x, that is, apply assignment: ai = ai - x, for all i.

The player who cannot make a move loses.

You're given the initial sequence a1, a2, ..., an. Determine who wins, if both players plays optimally well and if BitLGM and BitAryo start playing the described game in this sequence.

Input

The first line contains an integer n (1 ≤ n ≤ 3).

The next line contains n integers a1, a2, ..., an (0 ≤ ai < 300).

Output

Write the name of the winner (provided that both players play optimally well). Either "BitLGM" or "BitAryo" (without the quotes).

Examples
Input
2
1 1
Output
BitLGM
Input
2
1 2
Output
BitAryo
Input
3
1 2 1
Output
BitLGM
E. Sausage Maximization
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The Bitlandians are quite weird people. They have their own problems and their own solutions. They have their own thoughts and their own beliefs, they have their own values and their own merits. They have their own dishes and their own sausages!

In Bitland a sausage is an array of integers! A sausage's deliciousness is equal to the bitwise excluding OR (the xor operation) of all integers in that sausage.

One day, when Mr. Bitkoch (the local cook) was going to close his BitRestaurant, BitHaval and BitAryo, the most famous citizens of Bitland, entered the restaurant and each ordered a sausage.

But Mr. Bitkoch had only one sausage left. So he decided to cut a prefix (several, may be zero, first array elements) of the sausage and give it to BitHaval and a postfix (several, may be zero, last array elements) of the sausage and give it to BitAryo. Note that one or both pieces of the sausage can be empty. Of course, the cut pieces mustn't intersect (no array element can occur in both pieces).

The pleasure of BitHaval and BitAryo is equal to the bitwise XOR of their sausages' deliciousness. An empty sausage's deliciousness equals zero.

Find a way to cut a piece of sausage for BitHaval and BitAryo that maximizes the pleasure of these worthy citizens.

Input

The first line contains an integer n (1 ≤ n ≤ 105).

The next line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 1012) — Mr. Bitkoch's sausage.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

Print a single integer — the maximum pleasure BitHaval and BitAryo can get from the dinner.

Examples
Input
2
1 2
Output
3
Input
3
1 2 3
Output
3
Input
2
1000 1000
Output
1000