题目描述

It is a well-known fact that behind every good comet is a UFO. These UFOs often come to collect loyal supporters from here on Earth. Unfortunately, they only have room to pick up one group of followers on each trip. They do, however, let the groups know ahead of time which will be picked up for each comet by a clever scheme: they pick a name for the comet which, along with the name of the group, can be used to determine if it is a particular group's turn to go. The details of the matching scheme are given below; your job is to write a program which takes the names of a group and a comet and then determines whether the group should go with the UFO behind that comet.

Both the name of the group and the name of the comet are converted into a number in the following manner: the final number is just the product of all the letters in the name, where A is $1$ and Z is $26$. For instance, the group USACO would be $21 * 19 * 1 * 3 * 15 = 17955$. If the group's number mod $47$ is the same as the comet's number mod $47$, then you need to tell the group to get ready. Remember that "a mod b" is the remainder left over after dividing $a$ by $b$; $34$ mod $10$ is $4$.

Write a program which reads in the name of the comet and the name of the group and figures out whether according to the above scheme the names are a match, printing GO if they match and STAY if not. The names of the groups and the comets will be a string of capital letters with no spaces or punctuation, up to $6$ characters long.

输入格式

• Line 1: An upper case character string of length $1..6$ that is the name of the comet.
• Line 2: An upper case character string of length $1..6$ that is the name of the group.

Note: The input file has a newline at the end of each line but does not have a "return". Sometimes, programmers code for the Windows paradigm of "return" followed by "newline"; do not do that. Use simple input routines like readln (for Pascal) and, for C/C++, fscanf and fid>>string.

Note 2: Because of the extra characters, be sure to leave enough room for a newline (also notated as \n) and an end of string character (\0) if your language uses it (as C and C++ do). This means you need eight characters of room instead of six.

输出格式

A single line containing either the word GO or the word STAY.

COMETQ
HVNGAT

GO

ABSTAR
USACO

STAY

提示

Output Explanation

Converting the letters to numbers:

C O M E T Q
3 15 13 5 20 17

H V N G A T
8 22 14 7 1 20

Then calculate the product mod $47$:

3 * 15 * 13 * 5 * 20 * 17 = 994500 mod 47 = 27
8 * 22 * 14 * 7 * 1 * 20 = 344960 mod 47 = 27

Because both products evaluate to $27$ when modded by $47$, the mission is GO.

USACO Training Section 1.1.