<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>

<p>A <strong>split</strong> at an index <code>i</code> where <code>0 &lt;= i &lt;= n - 2</code> is called <strong>valid</strong> if the product of the first <code>i + 1</code> elements and the product of the remaining elements are coprime.</p>

<ul>
	<li>For example, if <code>nums = [2, 3, 3]</code>, then a split at the index <code>i = 0</code> is valid because <code>2</code> and <code>9</code> are coprime, while a split at the index <code>i = 1</code> is not valid because <code>6</code> and <code>3</code> are not coprime. A split at the index <code>i = 2</code> is not valid because <code>i == n - 1</code>.</li>
</ul>

<p>Return <em>the smallest index </em><code>i</code><em> at which the array can be split validly or </em><code>-1</code><em> if there is no such split</em>.</p>

<p>Two values <code>val1</code> and <code>val2</code> are coprime if <code>gcd(val1, val2) == 1</code> where <code>gcd(val1, val2)</code> is the greatest common divisor of <code>val1</code> and <code>val2</code>.</p>

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/12/14/second.PNG" style="width: 450px; height: 211px;" />
<pre>
<strong>Input:</strong> nums = [4,7,8,15,3,5]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The table above shows the values of the product of the first i + 1 elements, the remaining elements, and their gcd at each index i.
The only valid split is at index 2.
</pre>

<p><strong>Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/12/14/capture.PNG" style="width: 450px; height: 215px;" />
<pre>
<strong>Input:</strong> nums = [4,7,15,8,3,5]
<strong>Output:</strong> -1
<strong>Explanation:</strong> The table above shows the values of the product of the first i + 1 elements, the remaining elements, and their gcd at each index i.
There is no valid split.
</pre>

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

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution:
    def findValidSplit(self, nums: List[int]) -> int:
       #co prime if prefix elements do not share any primes with suffix elements

       #go through each prime
       # for each prime, get all numbers its apart of
       # if the number apart of is in nums: we set start, end to max,min of all occs of prime based on our number
       #add that to a line
       #then run sweepline till 0
        maxn = max(nums)
        line = [0]*len(nums)
        
        num_to_indices = defaultdict(list)
        for i,n in enumerate(nums):
            num_to_indices[n].append(i)

        is_prime = [False,False] + [True]*(maxn-1)

        for n in range(2,maxn+1):
            if is_prime[n]:
                start,end = len(nums),-1 
                if n in num_to_indices:
                    start = num_to_indices[n][0]
                    end = num_to_indices[n][-1]
                for j in range(n,maxn+1,n):
                    is_prime[j] = False
                    if j in num_to_indices:
                        start = min(start,num_to_indices[j][0])
                        end = max(end,num_to_indices[j][-1])
                
                if start != len(nums):
                    line[start] +=1
                    line[end] -=1

        t = 0
        for i in range(len(nums)-1):
            t += line[i]
            if t == 0:
                return i
        return -1

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