A boolean expression is an expression that evaluates to either true or false. It can be in one of the following shapes:

• 't' that evaluates to true.
• 'f' that evaluates to false.
• '!(subExpr)' that evaluates to the logical NOT of the inner expression subExpr.
• '&(subExpr1, subExpr2, ..., subExprn)' that evaluates to the logical AND of the inner expressions subExpr1, subExpr2, ..., subExprn where n >= 1.
• '|(subExpr1, subExpr2, ..., subExprn)' that evaluates to the logical OR of the inner expressions subExpr1, subExpr2, ..., subExprn where n >= 1.

Given a string expression that represents a boolean expression, return the evaluation of that expression.

It is guaranteed that the given expression is valid and follows the given rules.

 

Example 1:

Input: expression = "&(|(f))"
Output: false
Explanation: 
First, evaluate |(f) --> f. The expression is now "&(f)".
Then, evaluate &(f) --> f. The expression is now "f".
Finally, return false.

Example 2:

Input: expression = "|(f,f,f,t)"
Output: true
Explanation: The evaluation of (false OR false OR false OR true) is true.

Example 3:

Input: expression = "!(&(f,t))"
Output: true
Explanation: 
First, evaluate &(f,t) --> (false AND true) --> false --> f. The expression is now "!(f)".
Then, evaluate !(f) --> NOT false --> true. We return true.

 

Constraints:

• 1 <= expression.length <= 2 * 104
• expression[i] is one following characters: '(', ')', '&', '|', '!', 't', 'f', and ','.