Custom Expression Evaluator

Alice is creating her own expression calculator. The calculator evaluates infix expressions that consist of numbers, operators with custom priorities and associativities, and parentheses.

Token Definitions:

• Number Token: A sequence of one or more digits immediately followed by a dot ('.'). For example, 00123., 0., and 789. are valid.
• Operator Token: A sequence of one or more digits immediately followed by one of the characters: +, *, or ^. The digit part represents the operator's priority.

Operator Rules:

• The operator's priority (an integer) must lie between \(1\) and \(n\) inclusive, where \(n\) is the length of a given binary string \(C\).
• The given binary string \(C\) of length \(n\) specifies the associativity for each priority level. For the operator with priority \(p\), look at the \(p\)th character of \(C\): if it is 0 then the operator is left-associative; if it is 1 then it is right-associative.
• Operators have precedence according to their numerical priority; a higher number means a higher precedence.
• For operators with the same priority, use the associativity to decide the evaluation order. For example:
  Left-associative: 1.4+2.4^3.4^4. is evaluated as ((1 + 2) ^ 3) ^ 4.
  Right-associative: 1.6+2.6^3.6^4. is evaluated as 1 + (2 ^ (3 ^ 4)).
• Note: For exponentiation, the special case \(0^0 = 1\) is defined.

Expression Grammar:

1. A single number token is a valid infix expression.
2. If \(A\) is a valid expression, then \((A)\) is valid.
3. If \(A\) and \(B\) are valid expressions and \(c\) is a valid operator token, then the concatenation AcB is a valid infix expression.
4. All other forms are invalid.

Input: The first line contains a binary string \(C\) of length \(n\) (\(1 \le n \le 10^5\)) that defines the associativity of operators at each priority level. The second line contains the infix expression.

Output: If the expression is invalid, output error (without quotes). Otherwise, compute the value of the expression modulo \(998244353\) and output the result.

inputFormat

The input consists of two lines:

1. The first line is a binary string \(C\) which defines associativity for each priority. For a valid operator with priority \(p\), the \(p\)th character of \(C\) is 0 (left-associative) or 1 (right-associative).
2. The second line is a string representing the infix expression.

outputFormat

Output a single line. If the expression is invalid, output error. If it is valid, output the computed result modulo \(998244353\).

sample

10
123.

123