ZS the Coder has a large tree. It can be represented as an undirected connected graph of n vertices numbered from 0 to n - 1 and n - 1 edges between them. There is a single nonzero digit written on each edge.

One day, ZS the Coder was bored and decided to investigate some properties of the tree. He chose a positive integer M, which is coprime to 10, i.e. <image>.

ZS consider an ordered pair of distinct vertices (u, v) interesting when if he would follow the shortest path from vertex u to vertex v and write down all the digits he encounters on his path in the same order, he will get a decimal representaion of an integer divisible by M.

Formally, ZS consider an ordered pair of distinct vertices (u, v) interesting if the following states true:

  * Let a1 = u, a2, ..., ak = v be the sequence of vertices on the shortest path from u to v in the order of encountering them; 
  * Let di (1 ≤ i < k) be the digit written on the edge between vertices ai and ai + 1; 
  * The integer <image> is divisible by M. 



Help ZS the Coder find the number of interesting pairs!

Input

The first line of the input contains two integers, n and M (2 ≤ n ≤ 100 000, 1 ≤ M ≤ 109, <image>) — the number of vertices and the number ZS has chosen respectively.

The next n - 1 lines contain three integers each. i-th of them contains ui, vi and wi, denoting an edge between vertices ui and vi with digit wi written on it (0 ≤ ui, vi < n, 1 ≤ wi ≤ 9).

Output

Print a single integer — the number of interesting (by ZS the Coder's consideration) pairs.

Examples

Input

6 7
0 1 2
4 2 4
2 0 1
3 0 9
2 5 7


Output

7


Input

5 11
1 2 3
2 0 3
3 0 3
4 3 3


Output

8

Note

In the first sample case, the interesting pairs are (0, 4), (1, 2), (1, 5), (3, 2), (2, 5), (5, 2), (3, 5). The numbers that are formed by these pairs are 14, 21, 217, 91, 7, 7, 917 respectively, which are all multiples of 7. Note that (2, 5) and (5, 2) are considered different. 

<image>

In the second sample case, the interesting pairs are (4, 0), (0, 4), (3, 2), (2, 3), (0, 1), (1, 0), (4, 1), (1, 4), and 6 of these pairs give the number 33 while 2 of them give the number 3333, which are all multiples of 11.

<image>
import java.awt.Point;
import java.awt.geom.Line2D;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileReader;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.security.GuardedObject;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.io.InputStream;
import java.math.BigInteger;






/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */

public class Main {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
    
        
        OutputStream outputStream = System.out;
        FastScanner in;
        PrintWriter out;
        
           in=new FastScanner(System.in);
            out=new PrintWriter(System.out);
        //in=new FastScanner(new FileInputStream(new File("C://Users//KANDARP//Desktop//coding_contest_creation (1).txt")));
        
        TaskC solver = new TaskC();
        long var=System.currentTimeMillis();
        solver.solve(1, in, out);
        /*if(System.getProperty("ONLINE_JUDGE")==null){
            out.println("["+(double)(System.currentTimeMillis()-var)/1000+"]");
        }*/
        out.close();
    }
}
class Pair {
	
    long x,y,index;
    long  r1,r2;
    
    Pair(long x,long y,int index){
        this.x=x;
        this.y=y;
        this.index=index;
    }
    public String toString(){
        return this.x+" "+this.y+" ";
    }
    
}
class Edge implements  Comparable<Edge>{
    int u;
    int v;
    int time;
    long cost;
    long wcost;
    public Edge(int u,int v,long cost,long wcost){
        this.u=u;
        this.v=v;
        this.cost=cost;
        this.wcost=wcost;
        time=Integer.MAX_VALUE;
    }
    public int other(int x){
        if(u==x)return v;
        return u;
    }
    @Override
    public int compareTo(Edge o) {
        // TODO Auto-generated method stub
        return Long.compare(cost, o.cost);
    }
}
class queary{
    int type;
    int l;
    int r;
    int index;
    queary(int type,int l,int r,int index){
        this.type=type;
        this.l=l;
        this.r=r;
        this.index=index;
    }
}
class TaskC {
    static long mod=1000000007;
  static int prime_len=1000010;
    static int prime[]=new int[prime_len];
    static long n_prime[]=new long[prime_len];
    static ArrayList<Integer> primes=new ArrayList<>();
    static{ 
        for(int i=2;i<=Math.sqrt(prime.length);i++){
            for(int j=i*i;j<prime.length;j+=i){
                
                prime[j]=i;
                
            }
        }
        for(int i=2;i<prime.length;i++){
            n_prime[i]=n_prime[i-1];
            if(prime[i]==0){
               n_prime[i]++;
            }
            
        }
    //  System.out.println("end");
        
    //  prime[0]=true;
    //  prime[1]=1;
    }
    /*
       long pp[]=new long[10000001];
            pp[0]=0;
            pp[1]=1;
            for(int i=2;i<pp.length;i++){
                if(prime[i]!=0){
                    int gcd=(int)greatestCommonDivisor(i/prime[i], prime[i]);
                    pp[i]=(pp[i/prime[i]]*pp[prime[i]]*gcd)/pp[(int)gcd];
                }
                else
                    pp[i]=i-1;
            }
        

}
     * */
    
    class TrieNode{
    	int value;
    	TrieNode children[];
    	public TrieNode(int value,TrieNode children[] ){
    		this.value=value;
    		this.children=children;
    	}
    }
    class Trie{
    	TrieNode root;
    	int count;
    	public Trie(TrieNode root,int count){
    		this.root=root;
    		this.count=count;
    	}
    }
    public void insert(Trie t,char key[]){
    	t.count++;
    	int length=key.length;
    	int level=0;
    	TrieNode current=t.root;
    	if(current==null){
    		t.root=new TrieNode(0, new TrieNode[26]);
    		current=t.root;
    	}
    	for(level=0;level<length;level++){
    		int index=key[level]-'a';
    		if(current.children[index]==null){
    			current.children[index]=new TrieNode(0,new TrieNode[26]);
    		}
    		current=current.children[index];
    	}
    	current.value=t.count;
    }
    public int search(Trie t,char key[]){
    	TrieNode current=t.root;
    	if(current==null){
    		return 0;
    	}
    	int length=key.length;
    	int level=0;
    	for(level=0;level<length;level++){
    		int index=key[level]-'a';
    		if(current.children[index]==null){
    			return 0;
    		}
    		current=current.children[index];
    	}
    	return current.value;
    }
    class point{
    	int x;
    	int y;
    }
    int orientation(point p, point q, point r)
    {
        int val = (q.y - p.y) * (r.x - q.x) -
                  (q.x - p.x) * (r.y - q.y);
     
        if (val == 0) return 0;  // colinear
        return (val > 0)? 1: 2; // clock or counterclock wise
    }
    //int arr[]=new int[1000000000];
    int size[];
    int parent[];
    long ans=0;
    int m;
    ArrayList<Edge> adj[];
    public void dfs1(int index,int p){
    	size[index]=1;
    	parent[index]=p;
    	for(Edge x:adj[index]){
    		if(x.other(index)!=p){
    			dfs1(x.other(index),index);
    			size[index]+=size[x.other(index)];
    		}
    	}
    }
    long[] inv10Pow;
	long[] just10Pow;
    public void solve(int testNumber, FastScanner in, PrintWriter out) throws IOException {
    	int n=in.nextInt();
    	m=in.nextInt();
    	if (m == 1) {
			out.println((long) n * (n - 1));
			return;
		}

    	adj=new ArrayList[n];
    	for(int i=0;i<n;i++)
    		adj[i]=new ArrayList<>();
    	for(int i=0;i<n-1;i++){
    		int u=in.nextInt();
    		int v=in.nextInt();
    		int cost=in.nextInt()%m;
    		adj[u].add(new Edge(u, v, cost, cost));
    		adj[v].add(new Edge(v, u, cost, cost));
    		
    	}
    	int inv10 = BigInteger.TEN.modInverse(BigInteger.valueOf(m)).intValue();
    	inv10Pow=new long[n+1];
    	just10Pow=new long[n+1];
    	inv10Pow[0]=1;
    	just10Pow[0]=1;
    	for(int i=1;i<=n;i++){
    		inv10Pow[i]=((long)inv10Pow[i-1]*inv10)%m;
    	}
    	
    	for(int i=1;i<=n;i++){
    		just10Pow[i]=((long)just10Pow[i-1]*10L)%m;
    	}
    	parent=new int[n+1];
    	size=new int[n+1];
    	fun(0);
    	
    	out.println(ans);
    	
    }
    void removeAdj(ArrayList<Edge> adj,int u, int v) {
		for (int i = 0; i < adj.size(); i++) {
			if (v == adj.get(i).other(u)) {
				adj.set(i, adj.get(adj.size() - 1));
				adj.remove(adj.size() - 1);
				return;
			}
		}
		throw new AssertionError();
	}
    public void dfs2(int i,int p,int depth,int downRem,int upRem,HashMap<Integer,Integer> map,ArrayList<Integer> list,boolean countRoot){
    	if (countRoot) {
			if (downRem == 0) {
//		System.out.println("hi"+ i+" "+p);
				ans++;
			}
	
			if (upRem == 0) {
	//			System.out.println("hi"+ i+" "+p);
				
				ans++;
			}
		}
		
		list.add(upRem);

		int seek = downRem == 0 ? 0 : m - downRem;
		seek = (int) ((long) (seek * inv10Pow[depth]) % m);

		Integer delta = map.get(seek);
		if (delta != null) {
		//System.out.println(""+delta);
			ans += delta;
		}

		for (Edge e : adj[i]) {
			if (e.other(i) == p) {
				continue;
			}
			dfs2(e.other(i), i, depth + 1, (int) ((10L * downRem + e.cost) % m),
					(int) ((((long) just10Pow[depth] * e.cost )%m+ upRem) % m), map,
					list, countRoot);
		}
    }
    public void fun2(int i){
    	{
			HashMap<Integer, Integer> map = new HashMap<>();
			for (int j = 0; j < adj[i].size(); j++) {
				Edge e = adj[i].get(j);
				ArrayList<Integer> lst = new ArrayList<>();
				dfs2(e.other(i), i, 1, (int)e.cost, (int)e.cost, map, lst, true);

				for (int key : lst) {
					Integer prev = map.get(key);
					if (prev == null) {
						prev = 0;
					}
					map.put(key, prev + 1);
				}
			}
		}
		{
			HashMap<Integer, Integer> map = new HashMap<>();
			for (int j = adj[i].size()-1; j >=0; j--) {
				Edge e = adj[i].get(j);
				ArrayList<Integer> lst = new ArrayList<>();
				dfs2(e.other(i), i, 1, (int)e.cost, (int)e.cost, map, lst, false);

				for (int key : lst) {
					Integer prev = map.get(key);
					if (prev == null) {
						prev = 0;
					}
					map.put(key, prev + 1);
				}
			}
		}
    }
    public void fun(int i){
    	dfs1(i,-1);
    	int center=i;
    	LL:
    	while(true){
    		for(Edge x:adj[center]){
    			int y=x.other(center);
    			if(y!=parent[center] && 2*size[y]>=size[i]){
    				center=y;
    				continue LL;
    				
    			}
    		}
    		break;
    	}
    	//System.out.println(center);
    	fun2(center);
    	for(Edge x:adj[center]){
    		removeAdj(adj[x.other(center)], x.other(center), center);
    		fun(x.other(center));
    	}
    }
    
     public long getAns(int d[],int n){
    	 if(d[0]<0 && d[n-1]>0){
     		
     		return Math.min(-2*d[0]+d[n-1], 2*d[n-1]-d[0]);
     		
     		
     	 }
     	 else{
     		 if(d[0]<0){
     				return d[0]*-1;
     		 }
     		 else{
     				return(d[n-1]*1);
     		 }
     	 }
     	 
    	// return 0;
     }
     public boolean isTriangle(int x,int y,int z){
    	 if(x+y>z && x+z>y && y+z>x){
    		 return true;
    	 }
    	 return false;
     }
     public long optimize(long x){
    	 long y=x;
    	 if(x%10<5){
    		 x=x-x%10;
    		 
    	 }
    	 else{
    		 x=x+(10-x%10);
    	 }
    	 return y-x;
     }
   public static long[][] matrixexpo(long m[][],String n,long mod){
       if(n.equals("1")){
           return m.clone(); 
       }
       if(n.equals("10")){
           return mulmatrix(m, m , mod);
       }
       else{
           long temp [][]=matrixexpo(m,n.substring(0,n.length()-1),mod);
           temp=mulmatrix(temp, temp, mod);
           if(n.charAt(n.length()-1)=='0')return temp;
           else return mulmatrix(temp, m,mod);
       }
   }
   
	public static long[] mul(long[] a, long[] b)
	{
		int n = Math.max(a.length, b.length);
		int h = Integer.highestOneBit(n);
		if(n > h)h *= 2;
		if(a.length < h)a = Arrays.copyOf(a, h);
		if(b.length < h)b = Arrays.copyOf(b, h);
		return mul2(a, b, 0, h, 0, h);
	}
	
	public static long[] mul2(long[] a, long[] b, int al, int ar, int bl, int br)
	{
		int n = ar-al;
		if((n&n-1) != 0)throw new RuntimeException();
		if(n <= 1<<6){
			long[] res = muln(a, b, al, ar, bl, br);
			return res;
		}
		
		long[] c0 = mul2(a, b, al+0, al+n/2, bl+0, bl+n/2);
		long[] c2 = mul2(a, b, al+n/2, al+n, bl+n/2, bl+n);
		
		long[] ab0 = new long[n/2];
		long[] ab1 = new long[n/2];
		for(int i = 0;i < n/2;i++){
			ab0[i] = a[al+i] + a[al+i+n/2];
			ab1[i] = b[bl+i] + b[bl+i+n/2];
			if(ab0[i] >= mod)ab0[i] -= mod;
			if(ab1[i] >= mod)ab1[i] -= mod;
		}
		
		int e = n+c2.length;
		long[] ret = new long[e];
		for(int i = 0;i < c0.length;i++){
			ret[i] += c0[i];
			if(ret[i] >= mod)ret[i] -= mod;
		}
		for(int i = 0;i < c2.length;i++){
			ret[i+n] += c2[i];
			if(ret[i+n] >= mod)ret[i+n] -= mod;
		}
		
		long[] c1 = mul2(ab0, ab1, 0, n/2, 0, n/2);
		for(int i = 0;i < c1.length;i++){
			c1[i] -= c0[i] + c2[i];
			if(c1[i] < 0)c1[i] += mod;
			if(c1[i] < 0)c1[i] += mod;
		}
		for(int i = 0;i < c1.length;i++){
			ret[i+n/2] += c1[i];
			if(ret[i+n/2] >= mod)ret[i+n/2] -= mod;
		}
		return ret;
	}
	
	public static long[] muln(long[] a, long[] b, int al, int ar, int bl, int br)
	{
		int n = ar - al;
		long[] ret = new long[2*n];
		for(int i = 0;i < 2*n;i++){
			long tot = 0;
			for(int j = Math.max(i-n+1, 0);j <= i && j < n;j++){
				tot += a[al+j] * b[bl+i-j];
			}
			ret[i] = tot % mod;
		}
		return ret;
	}
	
   public static long[][] mulmatrix(long m1[][],long m2[][],long mod){
       long ans[][]=new long[m1.length][m2[0].length];
       for(int i=0;i<m1.length;i++){
           for(int j=0;j<m2[0].length;j++){
               for(int k=0;k<m1.length;k++){
                   ans[i][j]+=(m1[i][k]*m2[k][j]);
                   ans[i][j]%=mod;
               }
           }
       }
       return ans;
   }
   long pow(long x,long y,long mod){
       if(y<=0){
           return 1;
       }
       if(y==1){
           return x%mod;
       }
       long temp=pow(x,y/2,mod);
       if(y%2==0){
           return (temp*temp)%mod;
       }
       else{
           return (((temp*temp)%mod)*x)%mod;
       }
   }    
	    
   
	

   static long greatestCommonDivisor (long m, long n){
       long x;
       long y;
       while(m%n != 0){
           x = n;
           y = m%n;
           m = x;
           n = y;
       }
       return n;
   }
   static void dfs(List<Integer>[] graph, boolean[] used, List<Integer> res, int u,int parent,List<Integer> collection) {
       
       used[u] = true;
       Integer uu=new Integer(u);
       collection.add(uu);
       for (int v : graph[u]){
         if (!used[v]){
           dfs(graph, used, res, v,u,collection);
           
         }
         else if(collection.contains(v)){
             System.out.println("Impossible");
             System.exit(0);
         }
       }
       collection.remove(uu);
       res.add(u);
     }
   
       
     public static List<Integer> topologicalSort(List<Integer>[] graph) {
       int n = graph.length;
       boolean[] used = new boolean[n];
       List<Integer> res = new ArrayList<>();
       for (int i = 0; i < n; i++)
         if (!used[i])
           dfs(graph, used, res, i,-1,new ArrayList<Integer>());
       Collections.reverse(res);
       return res;
     }     
     
 }
	





 	
 
    class LcaSparseTable {

          int len;
          int[][] up;
          int[][] max;
          int[] tin;
          int[] tout;
          int time;
          int []lvel;
          
          void dfs(List<Integer>[] tree, int u, int p) {
            tin[u] = time++;
            lvel[u]=lvel[p]+1;
            up[0][u] = p;
            if(u!=p)
            //max[0][u]=weight(u,p);
            for (int i = 1; i < len; i++)
              {
                up[i][u] = up[i - 1][up[i - 1][u]];
                max[i][u]=Math.max(max[i-1][u],max[i-1][up[i-1][u]]);
              }
            for (int v : tree[u])
              if (v != p)
                dfs(tree, v, u);
            tout[u] = time++;
          }

          public LcaSparseTable(List<Integer>[] tree, int root) {
            int n = tree.length;
            len = 1;
            while ((1 << len) <= n) ++len;
            up = new int[len][n];
            max=new int[len][n];
            tin = new int[n];
            tout = new int[n];
            lvel=new int[n];
            lvel[root]=0;
            dfs(tree, root, root);
          }

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

          public 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];
          }
          public long max(int a,int b){
              int lca=lca(a,b);
        //    System.out.println("LCA "+lca);
              long ans=0;
              int h=lvel[a]-lvel[lca];
            //  System.out.println("Height "+h);
              int index=0;
              while(h!=0){
                  if(h%2==1){
                      ans=Math.max(ans,max[index][a]);
                      a=up[index][a];
                  }
                  h/=2;
                  index++;
              }
              h=lvel[b]-lvel[lca];
             // System.out.println("Height "+h);
              
              index=0;
              while(h!=0){ 
                  if(h%2==1){
                      ans=Math.max(ans,max[index][b]);
                      b=up[index][b];
                  }
                  h/=2;
                  index++;
              }
              return ans;
          }
          
    
        
            static void dfs1(List<Integer>[] graph, boolean[] used, List<Integer> res, int u) {
            used[u] = true;
            for (int v : graph[u])
              if (!used[v])
                dfs1(graph, used, res, v);
            res.add(u);
          }

        
        int phi(int n) {
            int res = n;
            for (int i = 2; i * i <= n; ++i) {
                if (n % i == 0) {
                    while (n % i == 0) {
                        n /= i;
                    }
                    res -= res / i;
                }
            }
            if (n != 1) {
                res -= res / n;
            }
            return res;
        }
        
        
        
        public static long[][] mulmatrix(long m1[][],long m2[][],long mod){
            long ans[][]=new long[m1.length][m2[0].length];
            for(int i=0;i<m1.length;i++){
                for(int j=0;j<m2[0].length;j++){
                    for(int k=0;k<m1.length;k++){
                        ans[i][j]+=(m1[i][k]*m2[k][j]);
                        ans[i][j]%=mod;
                    }
                }
            }
            return ans;
        }
        public static long[][] matrixexpo(long m[][],String n,long mod){
            if(n.equals("1")){
                return m.clone(); 
            }
            if(n.equals("10")){
                return mulmatrix(m, m , mod);
            }
            else{
                long temp [][]=matrixexpo(m,n.substring(0,n.length()-1),mod);
                temp=mulmatrix(temp, temp, mod);
                if(n.charAt(n.length()-1)=='0')return temp;
                else return mulmatrix(temp, m,mod);
            }
        }
        public static boolean isCompatible(long x[],long y[]){
            
            for(int i=0;i<x.length-1;i++){
                if(x[i]==y[i] && x[i+1]==y[i+1] && x[i]==x[i+1] && y[i]==y[i+1]){
                    return false;
                }
            }
            return true;
        }
        
        
        long pow(long x,long y,long mod){
            if(y<=0){
                return 1;
            }
            if(y==1){
                return x%mod;
            }
            long temp=pow(x,y/2,mod);
            if(y%2==0){
                return (temp*temp)%mod;
            }
            else{
                return (((temp*temp)%mod)*x)%mod;
            }
        }
     
        
                long no_of_primes(long m,long n,long k){
                    long count=0,i,j;
                    int primes []=new int[(int)(n-m+2)];
                       if(m==1)    primes[0] = 1;
                        for(i=2; i<=Math.sqrt(n); i++)
                        {
                            j = (m/i);    j *= i;
                            if(j<m)
                                j+=i;
                            for(; j<=n; j+=i)
                             {
                                 if(j!=i)
                                    primes[(int)(j-m)] = 1;
                             }
                        }

                for(i=0; i<=n-m; i++)
                            if(primes[(int)i]==0 && (i-1)%k==0)
                                count++;
                return count;
                }
                
}
    
class SegTree {
    int n;
    static long constt=Long.parseLong("111111111111111111111111111111",2);
    long  t[];
    long mod=(long)(1000000007);
    SegTree(int n,long  t[]){
        this.n=n;
        this.t=t;
        build();
    }
    
    void build() {  // build the tree
        
        for (int i = n - 1; i >= 0; --i){
            t[i]=(t[i<<1]&t[i<<1|1]);
          }
    }

     void modify(int p, long value) {  // set value at position p
      for (t[p += n]=value; p > 1; p >>= 1) t[p>>1] = (t[p]&t[p^1]);
    //  System.out.println(Arrays.toString(t));
     }

     long query(int l, int r) {  // sum on interval [l, r)
    	 long res=constt;
         
         for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
               if ((l&1)!=0) res=res&t[l++];
               if ((r&1)!=0) res=res&t[--r];
             }
         return res;
      
      
     }

    
    //  
//  
//  
}
class FastScanner
{

    private InputStream stream;
    private byte[] buf = new byte[8192];
    private int curChar;
    private int snumChars;
    private SpaceCharFilter filter;

    public FastScanner(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 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 boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}
 class UF {

    private int[] parent;  // parent[i] = parent of i
    private byte[] rank;   // rank[i] = rank of subtree rooted at i (never more than 31)
    private int count;     // number of components
    public UF(int N) {
        if (N < 0) throw new IllegalArgumentException();
        count = N;
        parent = new int[N];
        rank = new byte[N];
        for (int i = 0; i < N; i++) {
            parent[i] = i;
            rank[i] = 0;
        }
    }

    public int find(int p) {
        if (p < 0 || p >= parent.length) throw new IndexOutOfBoundsException();
        while (p != parent[p]) {
            parent[p] = parent[parent[p]];    // path compression by halving
            p = parent[p];
        }
        return p;
    }
    public int count() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public boolean union(int p, int q) {
        int rootP = find(p);
        int rootQ = find(q);
        if (rootP == rootQ) return false;

        // make root of smaller rank point to root of larger rank
        if      (rank[rootP] < rank[rootQ]) parent[rootP] = rootQ;
        else if (rank[rootP] > rank[rootQ]) parent[rootQ] = rootP;
        else {
            parent[rootQ] = rootP;
            rank[rootP]++;
        }
        count--;
        return true;
    }
    



}
 class MyScanner {
	   BufferedReader br;
	   StringTokenizer st;
	  
	   public MyScanner() {
	      br = new BufferedReader(new InputStreamReader(System.in));
	   }
	  
	   String next() {
	      while (st == null || !st.hasMoreElements()) {
	         try {
	            st = new StringTokenizer(br.readLine());
	         } catch (IOException e) {
	            e.printStackTrace();
	         }
	      }
	      return st.nextToken();
	   }
	  
	   int nextInt() {
	      return Integer.parseInt(next());
	   }
	  
	   long nextLong() {
	      return Long.parseLong(next());
	   }
	  
	   double nextDouble() {
	      return Double.parseDouble(next());
	   }
	  
	   String nextLine(){
	      String str = "";
	      try {
	         str = br.readLine();
	      } catch (IOException e) {
	         e.printStackTrace();
	      }
	      return str;
	   }
	 
	}