Maintain whether each slot currently contains a value and, when it does, the value itself.
Use a segment tree whose node stores both the minimum and maximum value in its interval. An interval containing no value is represented by a separate empty state. When merging two nodes, return the nonempty node if exactly one side is empty. If both are nonempty, store the smaller minimum and the larger maximum.
A type 1 query changes one leaf to a present value. A type 3 query changes one leaf to the empty state. A type 2 query merges the nodes covering the requested interval. Print nothing if the result is empty; otherwise print the product of its minimum and maximum.
Since each value has absolute value at most , the product can reach , so a 64-bit integer type is required.
The time complexity per test case is , and the space complexity is .
Solution written by GPT5.6
