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class Solution:
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    def pathSum(self, root: Optional[TreeNode], targetSum: int) -> int:
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        def util(node: TreeNode, sum_array) -> int:
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            t = [e - node.val for e in sum_array]
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            zeroes = t.count(0)
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            if node.left is None and node.right is None:
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                return zeroes
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            ansl, ansr = 0, 0
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            if node.left:
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                ansl = util(node.left, t + [targetSum])
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            if node.right:
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                ansr = util(node.right, t + [targetSum])
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            return ansl + ansr + zeroes
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        return util(root, [targetSum]) if root is not None else 0