You are given a string containing only parentheses ('(' and ')') and digits (0-9). At the index of a digit, you must delete a number of parentheses to the left of the index equal to the digit's value. Return true if it is possible to balance the parenthesis of the input.

Example 1 Input: ((2)) Output: False Reason: Only possible string is unbalanced: "))"

Example 2 Input: ((((2)) Output: True Reason: Only possible string is balanced: "(())"

Example 3 Input: (()1(1)) Output: True Reason: Multiple possible strings and one is balanced: ")())", "(())", "()))".

Background: 

1.Digits should not be included in the result string, although that doesn't matter for calculating the boolean result.

2.If a digit doesn't have enough characters to the left to delete, then return false.