**Cryptarithmetic Puzzle**

A cryptarithm is an arithmetic formula in which the digits are replaced by other symbols. Cryptarithms can be additions, multiplications, or divisions. For example,

SEND + MORE = MONEY

9567 + 1085 = 10652

WHO * IS = MOSIS

421 * 75 = 31575

LINK / NET = KT ... KEY

6041 / 453 = 13 ... 152

Conventionally following rules must be followed for the cryptarithms:

1. There must be a one-to-one mapping between symbols and digits.

2. When symbols are replaced by their digits, the formula must be correct.

3. The numerical base is 10.

4. Numbers must not begin with a zero.

5. There must be only one solution to the cryptarithm.

In this problem, you are going to solve cryptarithmetic additions that may have multiple addends. However, you should determine whether the cryptarithm has only one solution.

Input

There are multiple cryptarithms in the input file. Each line has one equation. On the right side of the equal sign, there is only one word. On the left side of the equal sign, there are two or more words, which are separated by plus signs. Each word consists of one or more uppercase letters. You may assume there are no more than 80 characters in a line.

Output

For each input, your program should print exactly one line of output. If the cryptarithm has exactly one solution, print the solution in which the letters of the cryptarithm are replaced by their digits. If the cryptarithm cannot be solved or it has more than one solution, print