<p>You are given a <strong>0-indexed</strong>&nbsp;array <code>nums</code> consisiting of <strong>positive</strong> integers. You can do the following operation on the array <strong>any</strong> number of times:</p>

<ul>
	<li>Select an index <code>i</code> such that <code>0 &lt;= i &lt; n - 1</code> and replace either of&nbsp;<code>nums[i]</code> or <code>nums[i+1]</code> with their gcd value.</li>
</ul>

<p>Return <em>the <strong>minimum</strong> number of operations to make all elements of </em><code>nums</code><em> equal to </em><code>1</code>. If it is impossible, return <code>-1</code>.</p>

<p>The gcd of two integers is the greatest common divisor of the two integers.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,6,3,4]
<strong>Output:</strong> 4
<strong>Explanation:</strong> 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].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,10,6,14]
<strong>Output:</strong> -1
<strong>Explanation:</strong> It can be shown that it is impossible to make all the elements equal to 1.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= nums.length &lt;= 50</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
</ul>

from math import gcd
from typing import List

class Solution:
    def minOperations(self, nums: List[int]) -> int:
        n = len(nums)
        
        # Count the number of 1s in the array
        num_ones = nums.count(1)
        
        # If there is at least one 1, we can spread it to the entire array
        if num_ones > 0:
            return n - num_ones
        
        # If there are no 1s, find the shortest subarray such that its gcd is 1
        min_len = n + 1
        for i in range(n):
            g = nums[i]
            for j in range(i + 1, n):
                g = gcd(g, nums[j])
                if g == 1:
                    min_len = min(min_len, j - i + 1)
                    break
        
        # If no such subarray exists, it's impossible to make all elements 1
        if min_len == n + 1:
            return -1
        
        # Otherwise, we can make the entire array 1 by first making the shortest subarray 1
        return n + min_len - 2

# Example usage:
solution = Solution()
print(solution.minOperations([2,6,3,4]))  # Output: 4
print(solution.minOperations([2,10,6,14])) # Output: -1
49