Given an integer amount and an array coins where each value represents a coin denomination, return the number of distinct combinations that sum exactly to amount. You may use each coin denomination in coins any number of times, and the order of coins in a combination does not matter.

Note: A combination is defined by the counts of each denomination used, not by the sequence in which coins are chosen.

Constraints:

• $1 \leq$ coins.length $\leq 300$

• $1 \leq$ coins[i] $\leq 5000$

• All values in coins are unique.

• $0 \leq$ amount $\leq 5000$

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