Widget Packing Validation

You are given a collection of widgets and a box. Each widget has a width, height, and weight. The box has dimensions given by its width, height, and depth. In addition, there is a maximum weight capacity for the box.

Your task is to determine if all the widgets can be fit into the box under the following conditions:

• The total weight of the widgets must not exceed the maximum weight.
• The widgets, when arranged side by side, have a combined width equal to the sum of all their widths and a combined height equal to the sum of all their heights. Using these, we calculate a combined volume as $$\text{combinedVolume} = \left(\sum_{i=1}^{n}width_i\right) \times \left(\sum_{i=1}^{n}height_i\right) \times depth_{box}.$$ This combined volume must not exceed the box's volume which is $$\text{boxVolume} = width_{box} \times height_{box} \times depth_{box}.$$

If both conditions are satisfied, the widgets can be successfully packed into the box; otherwise, they cannot.

inputFormat

The input is given via stdin in the following format:

1. An integer n representing the number of widgets.
2. Next, n lines follow; each contains three space-separated integers representing the width, height, and weight of a widget.
3. A line with three space-separated integers representing the box's width, height, and depth.
4. A single integer representing maxWeight, the maximum weight the box can handle.

outputFormat

Output a single line to stdout containing either True if the widgets can fit in the box, or False if they cannot.

2
2 3 4
2 3 4
5 10 3
15

True