Say that a "stair" in a list is a series of $3$ or more adjacent elements with equal distance between them, e$.$g$.[1,2,3]$ or $[10,12,14,16].$ So given an input list $[1,2,3,4,5,1,4,7],$ there are two stairs: $[1,2,3,4,5]$ and $[1,4,7].$

Print the number of stairs in an input list. $($You can hard$-$code the input list instead of reading it from the keyboard, e$.$g$.,$ setting the input list to be $[1,2,3,4,5,1,4,7]).$

Examples:

Input list $=[1,2,3,4,5,3,4,5,4]$

Output: $2$

Input list $=[1,1,3,5,1]$

Output: $1$

input list $=[1,1,2,1]$

Output: $0$