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北京大学《ACM-ICPC竞赛训练》暑期课面向全球招生。容量有限,报名从速!
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A hard Aoshu Problem
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 512Accepted: 256

Description

Math Olympiad is called “Aoshu” in China. Aoshu is very popular in elementary schools. Nowadays, Aoshu is getting more and more difficult. Here is a classic Aoshu problem:

ABBDE __ ABCCC = BDBDE


In the equation above, a letter stands for a digit(0 – 9), and different letters stands for different digits. After you fill the blank with '+', '-', '×' or '÷', and replace the letters with digits, you get an equation.

How to make the equation right? Here is a solution:

12245 + 12000 = 24245


In that solution, A = 1, B = 2, C = 0, D = 4, E = 5, and '+' is filled in the blank.

When I was a kid, finding a solution is OK. But now, my daughter’s teacher tells her to find all solutions. That’s terrible. I doubt whether her teacher really knows how many solutions are there. So please write a program for me to solve this kind of problems.

Input

The first line of the input is an integer T( T <= 20) indicating the number of test cases.

Each test case is a line which is in the format below:

s1 s2 s3

s1, s2 and s3 are all strings which are made up of capital letters. Those capital letters only include 'A','B','C','D' and 'E', so forget about 'F' to 'Z'. The length of s1,s2 or s3 is no more than 8.

When you put a '=' between s2 and s3, and put a operator('+', '-', '×' or '÷'.) between s1 and s2, and replace every capital letter with a digit, you get a equation.
You should figure out the number of solutions making the equation right.

Please note that same letters must be replaced by same digits, and different letters must be replaced by different digits. If a number in the equation is more than one digit, it must not have leading zero.

Output

For each test case, print an integer in a line. It represents the number of solutions.

Sample Input

2
A A A
BCD BCD B

Sample Output

5
72

Source

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