There are $n$ units indexed from $0$ to $n - 1$. You are given a $2 {D}$ integer array conversions of size $n - 1$, where conversions[i] = [sourceUnit_i, targetUnit_i, conversionFactor_i] indicates that $1$ unit of sourceUnit_i is equivalent to conversionFactor_i units of targetUnit_i.

Return an array of length $n$ where the $i {th}$ element is the number of units of type $i$ obtained from $1$ unit of type $0$.

Constraints:

• $2 \leq n \leq 10^5$

• conversions.length $= n - 1$

• $0 \leq$ sourceUnit_i, targetUnit_i $< n$

• $1 \leq$ conversionFactor_i $\leq 10^9$

• It is guaranteed that unit $0$ can be converted into any other unit through a unique combination of conversions without using any conversions in the opposite direction.

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