Walkthrough Example

Consider $n = 4$, edges: $1 \to 2$, $1 \to 3$, $2 \to 3$, $2 \to 4$, $3 \to 4$. Topological order: [$1$, $2$, $3$, $4$]. Initialize: $dp = [1, 0, 0, 0]$. Process level $1$: Update levels $2$ and $3$. $dp = [1, 1, 1, 0]$. Process level $2$: Update levels $3$ and $4$. dp[3] = (1 + 1) = 2, dp[4] = (0 + 1) = 1.

Now $dp = [1, 1, 2, 1]$. Process level $3$: Update level $4$. dp[4] = (1 + 2) = 3. Now $dp = [1, 1, 2, 3]$. Answer: dp[4] = 3 paths.