You are given an integer array cards of length 4. You have four cards, each containing a number in the range [1, 9]. You should arrange the numbers on these cards in a mathematical expression using the operators ['+', '-', '*', '/'] and the parentheses '(' and ')' to get the value 24.

You are restricted with the following rules:

The division operator '/' represents real division, not integer division.


    For example, 4 / (1 - 2 / 3) = 4 / (1 / 3) = 12.


Every operation done is between two numbers. In particular, we cannot use '-' as a unary operator.

    For example, if cards = [1, 1, 1, 1], the expression "-1 - 1 - 1 - 1" is not allowed.


You cannot concatenate numbers together

    For example, if cards = [1, 2, 1, 2], the expression "12 + 12" is not valid.

Return true if you can get such expression that evaluates to 24, and false otherwise.

  Example 1:

Input: cards = [4,1,8,7] Output: true Explanation: (8-4) * (7-1) = 24

Example 2:

Input: cards = [1,2,1,2] Output: false

  Constraints:

cards.length == 4
1 <= cards[i] <= 9