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Description
After hearing enough nonsense discussions, X decided to be short with the next problem's statement.
Given an array of length $n$, find out how many subarrays exist such that the difference between the maximum and minimum value is at least equal to the difference between the first and the last position of the subarray.
More formally, if we have the subarray $[L, R]$, whose maximum value is $A$ and whose minimum value is $B$, we want $A - B \geq R - L$.
The first line of the input contains $n$ ($1 \le n \le 2 \cdot 10^5$), the length of the array.
The next line of the input contains the array of length $n$, where $v_i$ ($1 \le v_i \le 2 \cdot 10^5$) is the $i_{th}$ value of the array.
The output will contain a single integer, representing the number of subarrays found.
Input
The first line of the input contains $n$ ($1 \le n \le 2 \cdot 10^5$), the length of the array.
The next line of the input contains the array of length $n$, where $v_i$ ($1 \le v_i \le 2 \cdot 10^5$) is the $i_{th}$ value of the array.
Output
The output will contain a single integer, representing the number of subarrays found.
7
1 2 3 1 1 3 2
12
4 2 3 1 2 3 4 5 6 4 6 1
17
43