Rules:

• each line starting with a "c" is considered a comment and thus skipped
• the first (non-comment) line contains a integer n [meaning: n is the number of variables]
• every following (non-comment) line (at most 10000 characters) represents a monomial. It contains a sequence of terms separated by  an arbitrary number of characters in the set (<space>, <tab>,  <comma>, <semicolon>)
• the first term is a real (in fixed or floating point representation) or an integer representing the weight of the monomial in the objective function (note that the objective function is always maximized)
• the following terms are integers in the range 1 ... n, representing the indices of all the variables appearing in the monomial
• a line containing only characters in the set (<space>, <tab>, <comma>, <semicolon>) does not provide the definition of any monomial, but is accepted

Example:

 maximize  5.2 x₁x₂x₄ - 2.1 x₁x₃ - 3.0 x₁x₂x₃ + 1.7 x₄

 
Input file:

c
c Binary Polynomial Optimization Instance
c
4
5.2   1 2 4
-2.1  1 3
-3.0  1 2 3
1.7   4