colors[i]:

colors[i] == 0 means that tile i is red.
colors[i] == 1 means that tile i is blue.

An alternating group is a contiguous subset of tiles in the circle with alternating colors (each tile in the group except the first and last one has a different color from its adjacent tiles in the group).

You have to process queries of two types:

queries[i] = [1, sizei], determine the count of alternating groups with size sizei.
queries[i] = [2, indexi, colori], change colors[indexi] to colori.

Return an array answer containing the results of the queries of the first type in order.

Note that since colors represents a circle, the first and the last tiles are considered to be next to each other.

Examples

Example 1:

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