You are given a $2$D integer array requests, where requests[i] $= [$ user_i, time_i $]$ indicates that user user_i made a request at time time_i. You are also given two integers k and window.

A subset of requests is valid if, for every user, no inclusive time range $[t, t +$ window $]$ contains more than k requests from that user for any time $t$.

Return the maximum number of requests that can be retained such that the resulting set of requests is valid.

Constraints:

• $1 \leq$ requests.length $\leq 10^5$

• requests[i] $= [$ user_i, time_i $]$

• $1 \leq$ k $\leq$ requests.length

• $1 \leq$ user_i, time_i, window $\leq 10^5$

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