Question in Problem QSET

general
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1

Hello,

I have query in below question/problem.
https://www.codechef.com/problems/QSET

Here @akumar3 has posted a solution.

Here is the solution link.

https://www.codechef.com/viewsolution/5863202

For that solution I am not able to understand below line.

Node mergeNodes(Node left, Node right) {
		Node res;
		res.sum = (left.sum + right.sum) % 3; 
		for (int i = 0; i < 3; i++) {
			res.remainder[i] += left.remainder[i];
			res.remainder[(i + left.sum) % 3] += right.remainder[i];
		}

		return res;
	}

I know we are combining nodes here. Let me explain you in example.
Let say we have a string “12”
So we are counting prefixes here.
for 1 = remainder = [0,1,0]
for 12 = remainder = [1,0,0]
Final remainder = [1,1,0]

But when we take separate 1, then remainder = [0,1,0] and for separate 2, then remainder = [0,0,1]. So how can we combine both of these array to get
remainder = [1,1,0]. What we are doing inside the loop?

I know the answer we are getting here. But I am not able to understand how we are getting the answer?

Can anybody please explain this code?