## 27 Oct PMCA Saturday 18:30 Python Homework 22.10.22.

**Question:**

Before being an ubiquous communications gadget, a mobile was just a structure made of strings and wires suspending colourfull things. This kind of mobile is usually found hanging over cradles of small babies.

The figure illustrates a simple mobile. It is just a wire, suspended by a string, with an object on each side. It can also be seen as a kind of lever with the fulcrum on the point where the string ties the wire. From the lever principle we know that to balance a simple mobile the product of the weight of the objects by their distance to the fulcrum must be equal. That is **W_{l} × D_{l} = W_{r} × D_{r}** where

**D**is the left distance,

_{l}**D**is the right distance,

_{r}**W**is the left weight and

_{l }**W**is the right weight.

_{r}In a more complex mobile the object may be replaced by a sub-mobile, as shown in the next figure. In this case it is not so straightforward to check if the mobile is balanced so we need you to write a program that, given a description of a mobile as input, checks whether the mobile is in equilibrium or not.

**Input Specification:**

The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also a blank line between two consecutive inputs.

The input is composed of several lines, each containing 4 integers separated by a single space. The 4 integers represent the distances of each object to the fulcrum and their weights, in the format:

**W_{l} D_{l} W_{r} D_{r} **

If **W_{l}** or

**W**is zero then there is a sub-mobile hanging from that end and the following lines define the the sub-mobile. In this case we compute the weight of the sub-mobile as the sum of weights of all its objects, disregarding the weight of the wires and strings. If both

_{r}**W**and

_{l}**W**are zero then the following lines define two sub-mobiles: first the left then the right one.

_{r}**Output Specification:**

For each test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line.

Write ‘YES’ if the mobile is in equilibrium, write ‘NO’ otherwise.

Sample Input 1 0 2 0 4 0 3 0 1 1 1 1 1 2 4 4 2 1 6 3 2 Sample Output YES

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