Manao has been to a tremendous candy shop several times. He has forgotten its exact placement, but remembers some information about each time he visited the shop.

The city Manao lives in can be represented as an infinite two-dimensional plane with a Cartesian coordinate system. From point (x, y), Manao can move to any of the points (x – 1, y), (x, y – 1), (x + 1, y), or (x, y + 1). In order to perform each of these 4 moves, he needs to walk 1 unit of length. Manao recalls that the candy shop was located at a point with integer coordinates. Also, he remembers that the i-th time he visited the candy shop, he went there from point (X[i]Y[i]) and walked at most R[i] units of length.

Since Manao’s visits to the shop span a long period of time, he may have misremembered some details. If no intersection complies with his reminiscence, return 0. Otherwise return the number of different intersections where Manao’s candy shop could be, assuming Manao remembers everything correctly.