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#include<map>
#include<queue>

BinaryTreeNode<int>* getparent(BinaryTreeNode<int>* root,int start, map<BinaryTreeNode<int>*,BinaryTreeNode<int>*>&parent){
    
    queue<BinaryTreeNode<int>*> q;
    parent[root]=NULL;
    q.push(root);
    BinaryTreeNode<int>* res=NULL;

    while(!q.empty()){
        BinaryTreeNode<int>* front=q.front();
        q.pop();

        if(front->data==start) res=front;

        if(front->left){
            parent[front->left]=front;
            q.push(front->left);
        }

        if(front->right){
            parent[front->right]=front;
            q.push(front->right);
        }    
    }
    return res;    
}

int timeToBurnTree(BinaryTreeNode<int>* root, int start)
{
    //DS
    if(root==NULL) return 0;
    map<BinaryTreeNode<int>*,BinaryTreeNode<int>*> parent; //(node,parent) to store parent
    map<BinaryTreeNode<int>*,bool> vis;  //to store if visited or not
    queue<BinaryTreeNode<int>*> q;
    //get parent array
    //find start node both done by getparent()
    BinaryTreeNode<int>* target = getparent(root,start,parent); //target node acquired

    //burning starts here !!!
    q.push(target);
    vis[target]=true;
    int ans=0;
    while(!q.empty()){
        //int ans=0;
        bool flag=0;
        for(int i=0;i<q.size();i++){
            BinaryTreeNode<int>* front=q.front();
            q.pop();

            if(front->left && !vis[front->left]) {
                q.push(front->left);
                vis[front->left]=true;
                flag=true;
            }

            if(front->right && !vis[front->right]) {
                q.push(front->right);
                vis[front->right]=true;
                flag=true;
            }
            if(parent[front]!=NULL && !vis[parent[front]]) {
                q.push(parent[front]);
                vis[parent[front]]=true;
                flag=true;
            }
        }
        if(flag==true) ans++;
    }
    return ans;
}