Given a $0$ indexed integer array nums, calculate the total sum of the beauty of nums[i] for all indices i satisfying $1 \leq$ i $\leq$ nums.length $- 2$.

For each index i in the range $1 \leq$ i $\leq$ nums.length $- 2$, the beauty of nums[i] is defined as:

• $2$, if for every index j with $0 \leq$ j $<$ i and every index k with i $<$ k $\leq$ nums.length $- 1$, the condition nums[j] $<$ nums[i] $<$ nums[k] holds true.

• $1$, if the previous condition is not satisfied, but nums[i - 1] $<$ nums[i] $<$ nums[i + 1] holds true.

• $0$, if none of the above conditions hold true.

Return the sum of the beauty of nums[i] for all valid indices i.

Constraints:

• $3 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^5$

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