You are to process a sequence of M queries of two types:
- Add a quadratic function f(x) = ax2 + bx + c into the plane.
- Compute the global minimum value of all the quadratic functions at x: min{fi(x)}.
The first line consists of one integer: M (number of queries). (2 ≤ M ≤ 106)
The next M lines contain queries. Each query can be either addition or computation.
- I a b c : add a quadratic function into the plane. You can assume the coefficient of the linear term is the double of the quadratic term's.
- Q x : compute the global minimum value of all the quadratic functions at x: min{fi(x)}. Before the query, there is at least a curve in the plane.
All numbers in the input file are integers, whose absolute values are no more than 10
6.
For each computation query, print a line consisting of one integer which denotes the global minimum value. Assume the absolute values of the answers are no more than 2 × 109.