<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 __init__(self):
        self.cache = {}
        self.primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]

    def findValidSplit(self, nums: List[int]) -> int:
        primeRanges = {}
        index = 0
        for num in nums:
            primeFactors = self.getPrimeFactors(num)
            for factor in primeFactors:
                r = primeRanges.get(factor)
                if r == None:
                    primeRanges[factor] = [index, index]
                primeRanges[factor][1] = index
            index += 1
        sortedRanges = sorted(list(primeRanges.values()))
        splitAt = 0
        for r in sortedRanges:
            if r[0] > splitAt:
                return splitAt
            if r[1] > splitAt:
                splitAt = r[1]
        if splitAt == len(nums) - 1:
            return -1
        else:
            return splitAt

    def getPrimeFactors(self, num: int) -> List[int]:
        factors = self.cache.get(num)
        if factors != None:
            return factors
        self.cache[num] = []
        maxVal = int(num ** 0.5)
        origNum = num
        for prime in self.primes:
            if prime > maxVal:
                break
            if num % prime == 0:
                self.cache[origNum].append(prime)
                num //= prime
            while num % prime == 0:
                num //= prime
            if num == 1:
                break
        if num != 1:
            self.cache[origNum].append(num)
        return self.cache[origNum]


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