Transformer Voltage Stability

The first line of input contains an integer 'N', the number of transformers (nodes).
The second line contains 'N' space-separated integers, where the i-th integer is the voltage of node i.
The third line contains 'N' space-separated integers, representing a parent array. The i-th integer is the parent of node i. The root node has a parent of -1.

Print the string STABLE if every node in the tree satisfies the stability rule.
Otherwise, print the string UNSTABLE.

A node's descendants are all the nodes in its subtree, excluding the node itself.
A leaf node has no descendants. The sum and count of its descendants are both 0. A leaf node is always considered stable by definition.
The problem uses 0-based indexing for nodes.

Sample Input 1:

4
20 10 5 8
-1 0 0 1

Sample Output 1:

STABLE

Explanation for Sample 1:

The tree structure is: 0 is the root with children 1 and 2. Node 1 has a child 3.
- Node 3 (leaf): Stable by definition.
- Node 2 (leaf): Stable by definition.
- Node 1: Has one descendant, node 3 (voltage 8). Average = 8/1 = 8. Node 1's voltage is 10. Since `8 < 10`, node 1 is stable.
- Node 0: Has three descendants: 1, 2, and 3 (voltages 10, 5, 8). Sum = 23, Count = 3. Average = 23/3 ≈ 7.67. Node 0's voltage is 20. Since `7.67 < 20`, node 0 is stable.
Since all nodes are stable, the entire network is STABLE.

Sample Input 2:

3
5 8 6
-1 0 0

Sample Output 2:

UNSTABLE

Explanation for Sample 2:

The tree has root 0 with children 1 and 2.
- Node 1 (leaf): Stable.
- Node 2 (leaf): Stable.
- Node 0: Has two descendants: 1 and 2 (voltages 8, 6). Sum = 14, Count = 2. Average = 14/2 = 7. Node 0's voltage is 5. The condition `7 < 5` is false.
Since node 0 is not stable, the entire network is UNSTABLE.

Expected Time Complexity:

The expected time complexity is O(N).

Constraints:

1 <= N <= 10^5
1 <= voltage <= 10^9

Time limit: 1 sec