Misha and Grisha are funny boys, so they like to use new underground. The underground has n stations connected with n - 1 routes so that each route connects two stations, and it is possible to reach every station from any other.

The boys decided to have fun and came up with a plan. Namely, in some day in the morning Misha will ride the underground from station s to station f by the shortest path, and will draw with aerosol an ugly text "Misha was here" on every station he will pass through (including s and f). After that on the same day at evening Grisha will ride from station t to station f by the shortest path and will count stations with Misha's text. After that at night the underground workers will wash the texts out, because the underground should be clean. 

The boys have already chosen three stations a, b and c for each of several following days, one of them should be station s on that day, another should be station f, and the remaining should be station t. They became interested how they should choose these stations s, f, t so that the number Grisha will count is as large as possible. They asked you for help.

Input

The first line contains two integers n and q (2 ≤ n ≤ 105, 1 ≤ q ≤ 105) — the number of stations and the number of days.

The second line contains n - 1 integers p2, p3, ..., pn (1 ≤ pi ≤ n). The integer pi means that there is a route between stations pi and i. It is guaranteed that it's possible to reach every station from any other.

The next q lines contains three integers a, b and c each (1 ≤ a, b, c ≤ n) — the ids of stations chosen by boys for some day. Note that some of these ids could be same.

Output

Print q lines. In the i-th of these lines print the maximum possible number Grisha can get counting when the stations s, t and f are chosen optimally from the three stations on the i-th day.

Examples

Input

3 2
1 1
1 2 3
2 3 3


Output

2
3


Input

4 1
1 2 3
1 2 3


Output

2

Note

In the first example on the first day if s = 1, f = 2, t = 3, Misha would go on the route 1 <image> 2, and Grisha would go on the route 3 <image> 1 <image> 2. He would see the text at the stations 1 and 2. On the second day, if s = 3, f = 2, t = 3, both boys would go on the route 3 <image> 1 <image> 2. Grisha would see the text at 3 stations.

In the second examle if s = 1, f = 3, t = 2, Misha would go on the route 1 <image> 2 <image> 3, and Grisha would go on the route 2 <image> 3 and would see the text at both stations.
												import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.Iterator;
								public class Solution1 implements Runnable
								{
									static final long MAX = 1000000007L;
									static class InputReader
									{
										private InputStream stream;
										private byte[] buf = new byte[1024];
										private int curChar;
										private int numChars;
										private SpaceCharFilter filter;
										private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
								 
										public InputReader(InputStream stream)
										{
											this.stream = stream;
										}
										
										public int read()
										{
											if (numChars==-1) 
												throw new InputMismatchException();
											
											if (curChar >= numChars)
											{
												curChar = 0;
												try 
												{
													numChars = stream.read(buf);
												}
												catch (IOException e)
												{
													throw new InputMismatchException();
												}
												
												if(numChars <= 0)				
													return -1;
											}
											return buf[curChar++];
										}
									 
										public String nextLine()
										{
											String str = "";
								            try
								            {
								                str = br.readLine();
								            }
								            catch (IOException e)
								            {
								                e.printStackTrace();
								            }
								            return str;
										}
										public int nextInt()
										{
											int c = read();
											
											while(isSpaceChar(c)) 
												c = read();
											
											int sgn = 1;
											
											if (c == '-') 
											{
												sgn = -1;
												c = read();
											}
											
											int res = 0;
											do 
											{
												if(c<'0'||c>'9') 
													throw new InputMismatchException();
												res *= 10;
												res += c - '0';
												c = read();
											}
											while (!isSpaceChar(c)); 
											
											return res * sgn;
										}
										
										public long nextLong() 
										{
											int c = read();
											while (isSpaceChar(c))
												c = read();
											int sgn = 1;
											if (c == '-') 
											{
												sgn = -1;
												c = read();
											}
											long res = 0;
											
											do 
											{
												if (c < '0' || c > '9')
													throw new InputMismatchException();
												res *= 10;
												res += c - '0';
												c = read();
											}
											while (!isSpaceChar(c));
												return res * sgn;
										}
										
										public double nextDouble() 
										{
											int c = read();
											while (isSpaceChar(c))
												c = read();
											int sgn = 1;
											if (c == '-') 
											{
												sgn = -1;
												c = read();
											}
											double res = 0;
											while (!isSpaceChar(c) && c != '.') 
											{
												if (c == 'e' || c == 'E')
													return res * Math.pow(10, nextInt());
												if (c < '0' || c > '9')
													throw new InputMismatchException();
												res *= 10;
												res += c - '0';
												c = read();
											}
											if (c == '.') 
											{
												c = read();
												double m = 1;
												while (!isSpaceChar(c)) 
												{
													if (c == 'e' || c == 'E')
														return res * Math.pow(10, nextInt());
													if (c < '0' || c > '9')
														throw new InputMismatchException();
													m /= 10;
													res += (c - '0') * m;
													c = read();
												}
											}
											return res * sgn;
										}
										
										public String readString() 
										{
											int c = read();
											while (isSpaceChar(c))
												c = read();
											StringBuilder res = new StringBuilder();
											do 
											{
												res.appendCodePoint(c);
												c = read();
											} 
											while (!isSpaceChar(c));
											
											return res.toString();
										}
									 
										public boolean isSpaceChar(int c) 
										{
											if (filter != null)
												return filter.isSpaceChar(c);
											return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
										}
									 
										public String next() 
										{
											return readString();
										}
										
										public interface SpaceCharFilter 
										{
											public boolean isSpaceChar(int ch);
										}
									}
								 	
									public static void main(String args[]) throws Exception
									{
										new Thread(null, new Solution1(),"Solution1",1<<26).start();
									}
									ArrayList<Integer> adj[];
									long[] val;
									int[] depth;
									int[][] parent;
									boolean[] visited;
									int level = 20;
									int root = 1;
									static long gcd(long a, long b)
								    {
								        // Everything divides 0 
								        if (a == 0 || b == 0)
								           return 0;
								     
								        // base case
								        if (a == b)
								            return a;
								     
								        // a is greater
								        if (a > b)
								            return gcd(a-b, b);
								        return gcd(a, b-a);
								    }
								    
								    // method to return LCM of two numbers
								    static long lcm(long a, long b)
								    {
								        return (a*b)/gcd(a, b);
								    }
								    class Node{
								    	long val;
								    	int ind;
								    	Node(long val,int ind){
								    		this.val = val;
								    		this.ind = ind;
								    	}
								    }
								    int time = 0;
								    Pair[] node;
								    void dfs(int curr,int prev){
								    	depth[curr] = depth[prev] + 1;
								    	parent[curr][0] = prev;
								    	time++;
								    	node[curr].a= time;
								    	visited[curr] = true;
								    	Iterator<Integer> it =  adj[curr].iterator();
								    	while(it.hasNext()){
								    		int x=  it.next();
								    		if(!visited[x]){
								    			dfs(x,curr);
								    		}
								    	}
								    	time++;
								    	node[curr].b = time;
								    }
								    void precompute(){
								    	for(int i = 1;i < level;i++){
								    		for(int j = 1;j < adj.length;j++){
								    			if(parent[j][i-1] != -1){
								    				parent[j][i] = parent[parent[j][i-1]][i-1];
								    			}
								    		}
								    	}
								    }
								    int lca(int u,int v){
								    	if(depth[u] > depth[v]){
								    		int temp = u;
								    		u = v;
								    		v = temp;
								    	}
								    	int diff = depth[v] - depth[u];
								    	for(int i = 0;i < level;i++){
								    		if(((diff >> i) & 1) == 1){
								    			v = parent[v][i];
								    		}
								    	}
								    	if(u == v){
								    		return u;
								    	}
								    	for(int i = level-1;i >= 0;i--){
								    		if(parent[u][i] != parent[v][i]){
								    			u = parent[u][i];
								    			v = parent[v][i];
								    		}
								    	}
								    	return parent[u][0];
								    }
									public void run()
									{
										InputReader sc= new InputReader(System.in);
										PrintWriter w= new PrintWriter(System.out);
										int n = sc.nextInt();
										int m = sc.nextInt();
										adj=  new ArrayList[n+1];
										visited=  new boolean[n+1];
										depth= new int[n+1];
										parent=  new int[n+1][level];
										node = new Pair[n+1];
										for(int i = 0;i <= n;i++){
											adj[i] = new ArrayList();
										}
										for(int i = 2;i <= n;i++){
											int x=  sc.nextInt();
											adj[i].add(x);
											adj[x].add(i);
										}
										for(int i = 0;i < node.length;i++){
											node[i] = new Pair();
										}
										dfs(1,0);
										precompute();
										for(int i = 0;i < m;i++){
											int a = sc.nextInt();
											int b=  sc.nextInt();
											int c= sc.nextInt();
											int lca = lca(a,b) ^ lca(b,c) ^ lca(a,c);
											int max = Integer.MIN_VALUE;
											max = Math.max(max,cal(a,lca,b,c));
											max = Math.max(max,cal(b,lca,a,c));
											max = Math.max(max,cal(c,lca,b,a));
											w.println(max);
										}
										w.close();
									}
									int cal(int x,int lca,int y,int z){
										int temp = lca(lca,x);
										int ans = depth[x] - depth[temp] + depth[lca] - depth[temp] + 1;
										
										return ans;
									}
									static class Pair implements Comparable<Pair>{
										int a;
										int b;
										Pair(){}
										Pair(int a,int b){
											this.a = a;
											this.b = b;
											
										}
										public int compareTo(Pair p){
											return Integer.compare(this.b,p.b);
										}
									}
					}
