Algorithms and Data Structures

# Cryptarithmetic Puzzle

You are given three strings `a`, `b`, and `c`. Your task is to assign a digit to each character in such a way that the equation `a + b = c` holds. It is guaranteed that a valid digit assignment solution exists for the given strings.
A digit assignment is valid if it satisfies the following conditions:
1. Each character in the strings `a`, `b`, and `c` represents a unique digit from 0 to 9.
1. The resulting numbers should not have leading zeroes, except the number 0 which consists of one zero digit.

#### Input

The input consists of three lines, each containing a string. The strings `a`, `b`, and `c` consist only of lowercase English letters, and their lengths are between 1 and 15 (inclusive).
It is guaranteed that a valid digit assignment solution exists for the given equation.

#### Output

Print the three respective numbers in the same order.
If there are multiple valid digit assignments that satisfy the equation, you can output any of the valid solutions.

#### Examples

 Input Output send more money 9567 1085 10652 a b b 0 3 3

#### Constraints

Time limit: 0.8 seconds

Memory limit: 512 MB

Output limit: 1 MB