### Problem Statement

Suppose there is a triangle of digits like the following:

```74932
1325
457
92
1```

Each digit, with the exception of those in the top row, is equal to the last digit of the sum of its upper and upper-right neighboring digits.

You will be given a String[] questionMarkTriangle containing a triangle where only one digit in each row is known and all others are represented by '?'s (see example 0 for clarification). Each element of questionMarkTriangle represents a row of the triangle, and the rows are given from top to bottom. Each element contains exactly one digit ('0'-'9') and the remaining characters are all '?'s. Restore the triangle and return it as a String[] without '?'s.

### Definition

 Class: RevealTriangle Method: calcTriangle Parameters: String[] Returns: String[] Method signature: String[] calcTriangle(String[] questionMarkTriangle) (be sure your method is public)

### Constraints

-questionMarkTriangle will contain between 1 and 50 elements, inclusive.
-Element i (0 indexed) of questionMarkTriangle will contain exactly n-i characters, where n is the number of elements in questionMarkTriangle.
-Each element of questionMarkTriangle will contain exactly one digit ('0'-'9') and all others characters will be '?'s.

### Examples

0)

 ```{"4??", "?2", "1"}```
`Returns: {"457", "92", "1" }`
 Let's substitute '?'s with unknown variables: ```4ab c2 1 ``` Having done that, we start solving for the variables from the bottom to the top. First, we know that the last digit of (c + 2) is 1. Therefore, c must be 9: ```4ab 92 1 ``` Now we know that the last digit of (4 + a) is 9, which means a is 5: ```45b 92 1 ``` And, finally, the last digit of (5 + b) is 2, so b is 7.
1)

 `{"1"}`
`Returns: {"1" }`
2)

 `{"???2", "??2", "?2", "2"}`
`Returns: {"0002", "002", "02", "2" }`
3)

 `{"??5?", "??9", "?4", "6"}`
`Returns: {"7054", "759", "24", "6" }`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8215

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=12176&pm=8215

boba5551

#### Testers:

PabloGilberto , Yarin , Olexiy , ivan_metelsky

Simple Math