Short-circuit Logical Expression Evaluation

This problem involves evaluating a logical expression consisting of the two constant values 0 (false) and 1 (true), the binary operators & (AND) and | (OR), and parentheses. The usual operator precedence applies: parentheses first, then the & operator, and finally the | operator. Operators of the same precedence are evaluated left‐to‐right.

The twist in this problem is that the evaluation is performed with short-circuit rules as follows:

• For an expression of the form a&b: evaluate a first. If a = 0 then the whole expression evaluates to 0 and b is not evaluated. This counts as one short-circuit of type &.
• For an expression of the form a|b: evaluate a first. If a = 1 then the whole expression evaluates to 1 and b is not evaluated. This counts as one short-circuit of type |.

Important: If a short-circuited sub-expression is inside another expression that is itself short-circuited, then the inner short-circuit is not counted. For example, in 1|(0&1) the outer OR short-circuits so (0&1) is never evaluated and its potential short-circuit is not counted.

Your task is to compute the final value of the expression (either 0 or 1) and report the number of short-circuits that occurred for the two operators (& and |) during the evaluation.

inputFormat

The input consists of a single line containing a valid logical expression without any spaces. The expression may contain the characters 0, 1, &, | and parentheses ( and ).

You can assume that the expression is non-empty and syntactically correct.

outputFormat

Output a single line containing three integers separated by spaces:

• The final result of the expression (either 0 or 1).
• The number of short-circuits triggered by the AND (&) operator.
• The number of short-circuits triggered by the OR (|) operator.

sample

0|1&0

0 0 0