A tree rooted at node 0 is given as follows:

• The number of nodes is nodes;
• The value of the ith node is value[i];
• The parent of the ith node is parent[i].

Remove every subtree whose sum of values of nodes is zero.

Return the number of the remaining nodes in the tree.

 

Example 1:

Input: nodes = 7, parent = [-1,0,0,1,2,2,2], value = [1,-2,4,0,-2,-1,-1]
Output: 2

Example 2:

Input: nodes = 7, parent = [-1,0,0,1,2,2,2], value = [1,-2,4,0,-2,-1,-2]
Output: 6

 

Constraints:

• 1 <= nodes <= 104
• parent.length == nodes
• 0 <= parent[i] <= nodes - 1
• parent[0] == -1 which indicates that 0 is the root.
• value.length == nodes
• -105 <= value[i] <= 105
• The given input is guaranteed to represent a valid tree.