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# Valid Parentheses Again

Problem Description

Robin bought a sequence consist of characters `'('`, `')'`, `'{'`, `'}'`, `'['`, `']'`.

A sequence is valid if it follows any one of the following rule:

• An empty sequnce is valid.
• If X is valid sequence, then '(' + X + ')' or '{' + X + '}' or '[' + X + ']' is also valid.
• If X and Y are valid, then X + Y is also valid.
• His brother played with the sequence and misplaced some of the characters, those misplaced characters are denoted by '?' in string A.

Inorder to make the sequence valid again, he decided to replace the character '?'.

Your task is to determing the number of valid sequences that can be created by replacing '?'. Since the answer could be large output answer % 109 + 7.

Problem Constraints

2 <= |A| <= 150

Length of string A is always even.

Input Format

First and only argument is a string A.

Output Format

Return an integer denoting the number of valid sequences.

Example Input

Input 1:

` A = "??}(??"`

Input 2:

` A = "]???"`

Example Output

Output 1:

` 3`

Output 2:

` 0`

Example Explanation

Explanation 1:

Explanation 2:

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
Hints
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## Discussion

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