<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:
        l = len(nums)
        memo = {}
        def getFactors(n):
            num = n
            if n in memo:
                return memo[n]
            divisor = 2
            factors = []
            while divisor * divisor <= n:
                if n%divisor != 0:
                    divisor += 1
                else:
                    n //= divisor
                    factors.append(divisor)
            if n > 1:
                factors.append(n)
            memo[num] = factors
            return factors
        total = {}
        for n in nums:
            for f in getFactors(n):
                if f not in total.keys():
                    total[f] = 0
                total[f] += 1
        prefix = {}
        for i in range(0, l-1):
            for f in getFactors(nums[i]):
                if f not in prefix.keys():
                    prefix[f] = 0    
                prefix[f] += 1
                total[f] -= 1
                if total[f] == 0:
                    del prefix[f]
            if len(prefix.keys()) == 0:
                return i
        return -1
19200