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We always hope things in our lives will run smoothly, and having smooth arrays may help. An array of non-negative integers is -smooth if the sum of every set of consecutive integers is exactly . Unfortunately, not all arrays are -smooth. In fact, all -smooth arrays must contain a repeating pattern of length .
Any array can be made -smooth by changing its elements. In each change one element may be modified to any integer between and , inclusive. You want to make all of your arrays smooth, but you don’t want to make any more changes than necessary. So the question is: What is the minimum number of changes you have to make so that a given array would become -smooth?
The first line of input will consist of three integers of the form:
where is the size of the array.
The remainder of the file will consist of integers, , separated by white space.
All input will be within the following constraints:
Your program must output a single integer specifying the minimum number of changes that must be made in order to make the array smooth.
3 3 5 1 2 3
6 3 5 1 2 3 3 2 1
5 1 5 1 2 3 4 5