439. Ternary Expression Parser

Given a string representing arbitrarily nested ternary expressions, calculate the result of the expression. You can always assume that the given expression is valid and only consists of digits 0-9 , , : , T and F ( T and F represent True and False respectively).

Note:

1. The length of the given string is ≤ 10000.
2. Each number will contain only one digit.
3. The conditional expressions group right-to-left (as usual in most languages).
4. The condition will always be either T or F . That is, the condition will never be a digit.
5. The result of the expression will always evaluate to either a digit 0-9 , T or F .

Example 1:

Input:

 "T
2:3"
Output:

 "2"
Explanation:

 If true, then result is 2; otherwise result is 3.

Example 2:

Input:

 "F
1:T
4:5"
Output:

 "4"
Explanation:

 The conditional expressions group right-to-left. Using parenthesis, it is read/evaluated as:
             "(F 
 1 : (T 
 4 : 5))"                   "(F 
 1 : (T 
 4 : 5))"
          -> "(F 
 1 : 4)"                 or       -> "(T 
 4 : 5)"
          -> "4"                                    -> "4"

Example 3:

Input:

 "T
T
F:5:3"
Output:

 "F"
Explanation:

 The conditional expressions group right-to-left. Using parenthesis, it is read/evaluated as:
             "(T 
 (T 
 F : 5) : 3)"                   "(T 
 (T 
 F : 5) : 3)"
          -> "(T 
 F : 3)"                 or       -> "(T 
 F : 5)"
          -> "F"                                    -> "F"