Optimize a directed graph representing a neural network by selecting a root node that minimizes the number of edge reversals needed. The graph has n nodes numbered from 1 to n and n - 1 edges, where the ith edge connects node g_from[i] to node g_to[i].

Select any node as the root, then reverse as many edges as necessary to make all edges flow away from the root. Find the root node choice that requires the minimum number of edge reversals.

Example

g_nodes = 4
g_from = [1, 2, 3]
g_to   = [4, 4, 4]

The graph is:

2 → 4 ←1
     ↑
     3

If node 2 is selected as the root, edges 1 → 4 and 3 → 4 need to be reversed.

After reversal:

      2
      ↓
      4
    ↙   ↘
   3     1

Hence, the minimum number of edges to be inverted is 2.

Returns

int: the minimum number of edges that must be inverted.

Constraints

• 2 ≤ g_nodes ≤ 10^5
• 1 ≤ g_from[i], g_to[i] ≤ g_nodes
• g_from[i] ≠ g_to[i]