<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>

def prime_factor(n):
    k = int(math.sqrt(n)) +1
    s = set()
    for i in range(2,k):
        if n==1:
            break
        while(n%i==0):
            n = n/i
            s.add(i)
    if n!=1:
        s.add(n)
    return s


class Solution:
    def findValidSplit(self, nums: List[int]) -> int:
        n = len(nums)
        if n==1:
            return -1
        if nums[0]==1:
            return 0
        d = {}
        f = defaultdict(list)
        for i in range(n):
            d[nums[i]] = prime_factor(nums[i])
            for k in d[nums[i]]:
                f[k].append(i)
        i = 0
        min_split = -1
        while True:
            if nums[i]==1:
                i += 1
                continue
            split_pt = max([max(f[k]) for k in d[nums[i]]])
            if split_pt > min_split:
                min_split = split_pt
            i += 1
            if i > min_split:
                break
        return min_split if min_split<=n-2 else -1
        


        

        





        # n = len(nums)
        # left_product = 1
        # right_product = reduce(lambda x,y:x*y, nums)
        # for i in range(n-1):
        #     left_product = left_product*nums[i]
        #     right_product = right_product/nums[i]
        #     if gcd(left_product, right_product)==1:
        #         return i
        # return -1


        
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