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.util.*;
import java.io.*;
import java.math.BigInteger;
 
/**
 *
 * @author usquare
 */

public class ProblemB {
    
    static long mod = (int) (1e9+7);
    static InputReader in;
    static PrintWriter out;
    static int len;
    static int[][] up;
    static int[] tin;
    static int[] tout;
    static int time;
    static ArrayList<Integer>[] g;
    static int[] depth;
    
    static void dfs(int u, int p) {
        tin[u] = time++;
        up[0][u] = p;
        for (int i = 1; i < len; i++)
            up[i][u] = up[i - 1][up[i - 1][u]];
        for (int v :g[u])
            if (v != p){
                depth[v] = depth[u] + 1;
                dfs( v, u);
            }
        tout[u] = time++;
    }


    static boolean isParent(int parent, int child) {
        return tin[parent] <= tin[child] && tout[child] <= tout[parent];
    }

    static int lca(int a, int b) {
        if (isParent(a, b))
            return a;
        if (isParent(b, a))
            return b;
        for (int i = len - 1; i >= 0; i--)
            if (!isParent(up[i][a], b))
                a = up[i][a];
        return up[0][a];
    }

    static void preprocess(int n,int root){

        len = 1;
        while ((1 << len) <= n) ++len;
        up = new int[len][n];
        tin = new int[n];
        tout = new int[n];
        depth = new int[n];
        depth[root] = 0;
        dfs(root, root);
    }
    
    static void solve() {
        
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);  
        
        int n = in.nextInt();
        int q = in.nextInt();
        g = new ArrayList[n];
        
        for(int i = 0; i < n; i++) g[i] = new ArrayList<>();
        
        for(int i = 1; i < n; i++){
            int p = in.nextInt() - 1;
            g[p].add(i);
            g[i].add(p);
        }
        preprocess(n, 0);

        while(q-- > 0){
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            int c = in.nextInt() - 1;
            int ans = get(a, b, c);
            ans = max(ans, get(b, a, c));
            ans = max(ans, get(c, a, b));
            out.println(ans);
        }
        
        out.close();
        
    }
    
    static int get(int a, int b, int c){
        int ans = 0;
        boolean ab = isParent(a, b);
        boolean ba = isParent(b, a);
        boolean ac = isParent(a, c);
        boolean ca = isParent(c, a);
        boolean bc = isParent(b, c);
        boolean cb = isParent(c, b);
        int lab = lca(a, b);
        int lac = lca(a, c);
        int lbc = lca(b, c);
        
        if(b == c) return depth[a] + depth[b] - 2*depth[lab] + 1;
        
        if(ab && ac) return depth[lbc] - depth[a] + 1;
        if(ba && bc) return depth[a] - depth[lac] + 1;
        if(ca && cb) return depth[a] - depth[lab] + 1;
        if(isParent(lab,lac)){
            if(isParent(lac, lbc)) return depth[a] - depth[lac] + 1 + depth[lbc] - depth[lac];
            return depth[a] - depth[lac] + 1;
        }
        if(isParent(lac,lab)){
            if(isParent(lab, lbc)) return depth[a] - depth[lab] + 1 + depth[lbc] - depth[lab];
            return depth[a] - depth[lab] + 1;
        }
        
        return 1;
    }
    
    public static void main(String[] args) {
 
        new Thread(null,new Runnable() {
            @Override
            public void run() {
                try{
                    solve();
                }
                catch(Exception e){
                    e.printStackTrace();
                }
            }
        },"1",1<<26).start();
    }
    
    static class Pair implements Comparable<Pair>{
 
        int x,y;
        int i;
        
	Pair (int x,int y,int i){
		this.x=x;
		this.y=y;
		this.i=i;
	}
 
	Pair (int x,int i){
		this.x=x;
		this.i=i;
	}
        
	public int compareTo(Pair o) {
            return Long.compare(this.x,o.x);
		//return 0;
	}
 
            public boolean equals(Object o) {
            if (o instanceof Pair) {
                Pair p = (Pair)o;
                return p.x == x && p.y == y && p.i==i;
            }
            return false;
        }
 
        @Override
        public String toString() {
            return x+" "+y+" "+i;
        }
        
    } 
    
    static class Merge {
        
        public static void sort(long inputArr[]) {
            int length = inputArr.length;
            doMergeSort(inputArr,0, length - 1);
        }
        
        private static void doMergeSort(long[] arr,int lowerIndex, int higherIndex) {        
            if (lowerIndex < higherIndex) {
                int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
                doMergeSort(arr,lowerIndex, middle);
                doMergeSort(arr,middle + 1, higherIndex);
                mergeParts(arr,lowerIndex, middle, higherIndex);
            }
        }
        
        private static void mergeParts(long[]array,int lowerIndex, int middle, int higherIndex) {
            long[] temp=new long[higherIndex-lowerIndex+1];
            for (int i = lowerIndex; i <= higherIndex; i++) {
                temp[i-lowerIndex] = array[i];
            }
            int i = lowerIndex;
            int j = middle + 1;
            int k = lowerIndex;
            while (i <= middle && j <= higherIndex) {
                if (temp[i-lowerIndex] < temp[j-lowerIndex]) {
                    array[k] = temp[i-lowerIndex];
                    i++;
                } else {
                    array[k] = temp[j-lowerIndex];
                    j++;
                }
                k++;
            }
            while (i <= middle) {
                array[k] = temp[i-lowerIndex];
                k++;
                i++;
            }
            while(j<=higherIndex){
                array[k]=temp[j-lowerIndex];
                k++;
                j++;
            }
        }
 
    }
    
    static long add(long a,long b){
        long x=(a+b);
        while(x>=mod) x-=mod;
        return x;
    }
 
    static long sub(long a,long b){
        long x=(a-b);
        while(x<0) x+=mod;
        return x;
    }
    
    static long mul(long a,long b){
        a%=mod;
        b%=mod;
        long x=(a*b);
        return x%mod;
    }
 
    
    static boolean isPal(String s){
        for(int i=0, j=s.length()-1;i<=j;i++,j--){
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
    }
    static String rev(String s){
		StringBuilder sb=new StringBuilder(s);
		sb.reverse();
		return sb.toString();
    }
    
    static long gcd(long x,long y){
	if(y==0)
		return x;
	else
		return gcd(y,x%y);
    }
    
    static int gcd(int x,int y){
	if(y==0)
		return x;
	else 
		return gcd(y,x%y);
    }
    
    static long gcdExtended(long a,long b,long[] x){
        
        if(a==0){
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);
        
        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];
        
        return gcd;
    }
    
 
    static long mulmod(long  a,long b,long m) {
        if (m <= 1000000009) return a * b % m;
 
        long res = 0;
        while (a > 0) {
            if ((a&1)!=0) {
                res += b;
                if (res >= m) res -= m;
            }
            a >>= 1;
            b <<= 1;
            if (b >= m) b -= m;
        }
        return res;
    }
    
    static int abs(int a,int b){
	return (int)Math.abs(a-b);
    }
 
    public static long abs(long a,long b){
	return (long)Math.abs(a-b);
    }
    
    static int max(int a,int b){
	if(a>b)
		return a;
	else
		return b;
    }
 
    static int min(int a,int b){
	if(a>b)
		return b;
	else 
		return a;
    }
    
    static long max(long a,long b){
	if(a>b)
		return a;
	else
		return b;
    }
 
    static long min(long a,long b){
	if(a>b)
		return b;
	else 
		return a;
    }
 
    static long pow(long n,long p,long m){
	 long  result = 1;
	  if(p==0)
	    return 1;
          
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    if(result>=m)
	    result%=m;
	    p >>=1;
	    n*=n;
	    if(n>=m)
	    n%=m;
	}
	return result;
    }
    
    static long pow(long n,long p){
	long  result = 1;
	  if(p==0)
	    return 1;
          
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;	    
	    p >>=1;
	    n*=n;	    
	}
	return result;
    }
    
    static void debug(Object... o) {
            System.out.println(Arrays.deepToString(o));
    }
     
    static class InputReader {
    
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
                this.stream = stream;
        }
 
        public int snext() {
                if (snumChars == -1)
                        throw new InputMismatchException();
                if (curChar >= snumChars) {
                        curChar = 0;
                        try {
                                snumChars = stream.read(buf);
                        } catch (IOException e) {
                                throw new InputMismatchException();
                        }
                        if (snumChars <= 0)
                                return -1;
                }
                return buf[curChar++];
        }
 
        public int nextInt() {
                int c = snext();
                while (isSpaceChar(c)) {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                        sgn = -1;
                        c = snext();
                }
                int res = 0;
                do {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }
 
        public long nextLong() {
                int c = snext();
                while (isSpaceChar(c)) {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                        sgn = -1;
                        c = snext();
                }
                long res = 0;
                do {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }
 
        public int[] nextIntArray(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++) {
                        a[i] = nextInt();
                }
                return a;
        }
 
        public long[] nextLongArray(int n) {
                long a[] = new long[n];
                for (int i = 0; i < n; i++) {
                        a[i] = nextLong();
                }
                return a;
        }
 
        public String readString() {
                int c = snext();
                while (isSpaceChar(c)) {
                        c = snext();
                }
                StringBuilder res = new StringBuilder();
                do {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
        }
 
        public String nextLine() {
                int c = snext();
                while (isSpaceChar(c))
                        c = snext();
                StringBuilder res = new StringBuilder();
                do {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isEndOfLine(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;
        }
 
        private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
        }
        
    }
}    
 