Points and Rectangles Pair Counting

You are given an initially empty 2D plane. You need to process \(q\) queries. There are two types of queries:

• 1 x y — Add a point at coordinate \((x,y)\).
• 2 x_1 y_1 x_2 y_2 — Add a rectangle with the bottom‐left corner at \((x_1,y_1)\) and the top‐right corner at \((x_2,y_2)\). The rectangle's area may be \(0\) and it can degenerate to a point.

Note that points and rectangles may overlap. After each query, you are required to compute the total number of \( (\text{point}, \text{rectangle})\) pairs such that the point lies inside or on the boundary of the rectangle.

Note: A point \((x,y)\) is inside a rectangle defined by \((x_1,y_1)\) and \((x_2,y_2)\) if and only if \(x_1 \le x \le x_2\) and \(y_1 \le y \le y_2\).

inputFormat

The first line contains an integer \(q\) representing the number of queries. Each of the following \(q\) lines contains a query in one of the formats described above.

outputFormat

For each query, output a single line containing the total number of valid \((\text{point}, \text{rectangle})\) pairs after processing that query.

sample

3
1 0 0
2 -1 -1 1 1
1 2 2

0
1
1