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  1. All Contests
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  3. Jerry's Expression

Jerry's Expression

This problem revolves around the Polish notation.

  • Polish notation is the way to write parenthesis-free expressions. Its distinguishing feature is that it places operators to the left of their operands.
  • expression ::= number | (operator expression expression)
  • operator ::= | | | | …
  • For example: "" is "".

You are given a Polish notation expression. Operators can be only and . Each number in expression is replaced with . You have to replace each with positive integer number, so that value of expression was . Also, you have to make the biggest number in expression as small as possible.

Input Format

The only line contains string with expression (string will contain only '?', '+' and '-').

Constraints

  • string length .

Output Format

Return an integer array, number should be the number for '?' in the string. If there are many solutions print any.

Sample Input 0

-?-??

Sample Output 0

1
2
1

Explanation 0

- 1 - 2 1   is   1-(2-1) = 0