Construct a Valid Expression with Ones

Given a positive integer \(k\), construct a valid expression that uses only the characters 1, +, *, (, and ) such that:

• There are no two adjacent \(1\)'s.
• The total number of \(1\)'s is at most 100.
• The value of the expression is \(k\).

You are also given the formal definition of a valid expression:

• 1 is a valid expression.
• If a and b are valid expressions, then a+b, a*b, (a+b) and (a*b) are valid expressions.

If a valid expression satisfying the constraints exists, output it; otherwise, output no solution.

inputFormat

The input consists of a single line containing a positive integer \(k\).

Constraints:

• \(1 \le k \le 10^9\) (practically, only values for which a solution exists under the \(1\)'s limitation will be tested).

outputFormat

Output one line: the constructed valid expression that evaluates to \(k\) if one exists. If no valid expression exists, output no solution.

sample

1

1