Minimum Number of Operations to Make All Array Elements Equal to 1

Medium

You receive a 0-indexed array nums consisting of positive integers. You can do the following operation on the array any number of times:

Select an index i such that 0 <= i < n - 1 and replace either of nums[i] or nums[i+1] with their gcd value.

Produce the minimum number of operations to make all elements of nums equal to 1. If it is impossible, produce -1.

The gcd of two integers is the greatest common divisor of the two integers.

Example 1

Input: nums = [2,6,3,4]

Output: 4

Explanation: We can do the following operations:

Choose index i = 2 and replace nums[2] with gcd(3,4) = 1. Now we have nums = [2,6,1,4].
Choose index i = 1 and replace nums[1] with gcd(6,1) = 1. Now we have nums = [2,1,1,4].
Choose index i = 0 and replace nums[0] with gcd(2,1) = 1. Now we have nums = [1,1,1,4].
Choose index i = 2 and replace nums[3] with gcd(1,4) = 1. Now we have nums = [1,1,1,1].

Example 2

Input: nums = [2,10,6,14]

Output: -1

Explanation: It can be shown that it is impossible to make all the elements equal to 1.

Constraints