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A pair of positive integers (a, b) is said to be a coprime-twin pair, if for all positive integers x, both a and b and are coprime to x or both and are not coprime to x. Formally, 2 distinct positive integers a and b can form a coprime-twin pair if and only if S(a) = S(b), where S(x) denotes the set of all positive integers that are coprime to x.

For example:

2 and 4 are coprime-twin pairs.
1 and 2 are not coprime-twin pairs.


The score of a sequence a1, a2, .. an is the number of indices (i, j) such that i < j and the pair (ai, aj) forms a coprime-twin pair.

You are given an array A of positive integers and Q queries of the form L, R. For each query, determine the score of the subarray [L,  R] inclusive.

Note: A subarray is a contiguous non-empty segment of the array. 

An ant is at the bottom of the wall 35 feet down. It climbs up 2 feet each hour, but later it slips down 1 feet. How long will it take to reach the top of the wall?

You are given an array of integers. You need to sort the array in ascending order using quick sort.

Quick sort is a divide and conquer algorithm in which we choose a pivot point and partition the array into two parts i.e, left and right. The left part contains the numbers smaller than the pivot element and the right part contains the numbers larger than the pivot element. Then we recursively sort the left and right parts of the array.

Example:

Let the array = [ 4, 2, 1, 5, 3 ]
Let pivot to be the rightmost number.

After the 1st level partitioning the array will be { 2, 1, 3, 4, 5 } as 3 was the pivot. After 2nd level partitioning the array will be { 1, 2, 3, 4, 5 } as 1 was the pivot for the left part and 5 was the pivot for the right part. Now our array is sorted and there is no need to divide it again.

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What are the ACID properties. (Learn)

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