Anton likes to play chess. Also, he likes to do programming. That is why he decided to write the program that plays chess. However, he finds the game on 8 to 8 board to too simple, he uses an infinite one instead.

The first task he faced is to check whether the king is in check. Anton doesn't know how to implement this so he asks you to help.

Consider that an infinite chess board contains one white king and the number of black pieces. There are only rooks, bishops and queens, as the other pieces are not supported yet. The white king is said to be in check if at least one black piece can reach the cell with the king in one move. 

Help Anton and write the program that for the given position determines whether the white king is in check.

Remainder, on how do chess pieces move: 

  * Bishop moves any number of cells diagonally, but it can't "leap" over the occupied cells. 
  * Rook moves any number of cells horizontally or vertically, but it also can't "leap" over the occupied cells. 
  * Queen is able to move any number of cells horizontally, vertically or diagonally, but it also can't "leap". 

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 500 000) — the number of black pieces.

The second line contains two integers x0 and y0 ( - 109 ≤ x0, y0 ≤ 109) — coordinates of the white king.

Then follow n lines, each of them contains a character and two integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — type of the i-th piece and its position. Character 'B' stands for the bishop, 'R' for the rook and 'Q' for the queen. It's guaranteed that no two pieces occupy the same position.

Output

The only line of the output should contains "YES" (without quotes) if the white king is in check and "NO" (without quotes) otherwise.

Examples

Input

2
4 2
R 1 1
B 1 5


Output

YES


Input

2
4 2
R 3 3
B 1 5


Output

NO

Note

Picture for the first sample: 

<image> White king is in check, because the black bishop can reach the cell with the white king in one move. The answer is "YES".

Picture for the second sample: 

<image> Here bishop can't reach the cell with the white king, because his path is blocked by the rook, and the bishop cant "leap" over it. Rook can't reach the white king, because it can't move diagonally. Hence, the king is not in check and the answer is "NO".

import java.io.*;
import java.util.*;

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 A {
    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 implements Comparable<point>{
        long x;
        long y;
        public point(long x,long y){
            this.x=x;
            this.y=y;
        }
        @Override
        public int compareTo(point o) {
            // TODO Auto-generated method stub
            if(o.x==x && o.y==y)
                return 0;
            else return (int)Math.max(x-o.x, y-o.y);
        }
        public int hashCode(){
            return (int)(x+y);

        }
        public boolean equals(Object z){
            if(z!=null){
                point o=(point)z;
                if(o.x==x && o.y==y)
                    return true;
            }
            return false;
        }

    }
    class Edge {
        int t, rev, cap, f;

        public Edge(int t, int rev, int cap) {
            this.t = t;
            this.rev = rev;
            this.cap = cap;
        }
    }

    class MaxFlowDinic {


        public  List<Edge>[] createGraph(int nodes) {
            List<Edge>[] graph = new List[nodes];
            for (int i = 0; i < nodes; i++)
                graph[i] = new ArrayList<>();
            return graph;
        }

        public  void addEdge(List<Edge>[] graph, int s, int t, int cap) {
            graph[s].add(new Edge(t, graph[t].size(), cap));
            graph[t].add(new Edge(s, graph[s].size() - 1, 0));
        }

        boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
            Arrays.fill(dist, -1);
            dist[src] = 0;
            int[] Q = new int[graph.length];
            int sizeQ = 0;
            Q[sizeQ++] = src;
            for (int i = 0; i < sizeQ; i++) {
                int u = Q[i];
                for (Edge e : graph[u]) {
                    if (dist[e.t] < 0 && e.f < e.cap) {
                        dist[e.t] = dist[u] + 1;
                        Q[sizeQ++] = e.t;
                    }
                }
            }
            return dist[dest] >= 0;
        }

        int dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, int f) {
            if (u == dest)
                return f;
            for (; ptr[u] < graph[u].size(); ++ptr[u]) {
                Edge e = graph[u].get(ptr[u]);
                if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
                    int df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(f, e.cap - e.f));
                    if (df > 0) {
                        e.f += df;
                        graph[e.t].get(e.rev).f -= df;
                        return df;
                    }
                }
            }
            return 0;
        }

        public  int maxFlow(List<Edge>[] graph, int src, int dest) {
            int flow = 0;
            int[] dist = new int[graph.length];
            while (dinicBfs(graph, src, dest, dist)) {
                int[] ptr = new int[graph.length];
                while (true) {
                    int df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
                    if (df == 0)
                        break;
                    flow += df;
                }
            }
            return flow;
        }
    }
    //int arr[]=new int[1000000000];

    public void solve(int testNumber, FastScanner in, PrintWriter out) throws IOException {
       int n = in.nextInt();
       long x0 = in.nextLong();
       long y0 = in.nextLong();
       long x[] = new long[8];
       long y[] = new long[8];
       for(int i=0;i<8;i++){
           x[i] =Long.MIN_VALUE;
           y[i] =Long.MIN_VALUE;
       }
       String t[] = new String[8];
       for(int i=0;i<n;i++){

           String type = in.readString();
           long xc = in.nextLong();
           long yc  = in.nextLong();

           if(xc == x0 && yc>y0 && (y[0] > yc || y[0] == Long.MIN_VALUE)){
               x[0] = xc;
               y[0] = yc;
               t[0] = type;
           }
           else if(xc == x0 && yc < y0 && (y[1] < yc || y[1] == Long.MIN_VALUE)){
               x[1] = xc;
               y[1] = yc;
               t[1] = type;
           }
           else if(yc == y0 && xc >x0 && (x[2] > xc || x[2] == Long.MIN_VALUE)){
               x[2] = xc;
               y[2] = yc;
               t[2] = type;
           }
           else if(yc==y0 && xc < x0 && (x[3] < xc || x[3] == Long.MIN_VALUE)) {
               x[3] = xc;
               y[3] = yc;
               t[3] = type;
           }
           else if(x0+y0 == xc+yc && xc<x0 && (x[4] < xc || x[4] == Long.MIN_VALUE)){
               x[4] = xc;
               y[4] = yc;
               t[4] = type;
           }
           else if(x0+y0 == xc+yc && xc>x0 && (x[5] > xc || x[5] == Long.MIN_VALUE)){
               x[5] = xc;
               y[5] = yc;
               t[5] = type;
           }
           else if(x0-y0 == xc-yc && xc<x0 && (x[6] < xc || x[6] == Long.MIN_VALUE)){
               x[6] = xc;
               y[6] = yc;
               t[6] = type;
           }
           else if(x0-y0 == xc-yc && xc>x0 && (x[7] > xc || x[7] == Long.MIN_VALUE)){
               x[7] = xc;
               y[7] = yc;
               t[7] = type;
           }

       }
       for(int i=0;i<8;i++){
            if(t[i]!=null){
                if(t[i].equals("Q")){
                    out.println("YES");
                    return;
                }
                if(t[i].equals("B") && i>=4){
                    out.println("YES");
                    return;
                }
                if(t[i].equals("R") && i<4){
                    out.println("YES");
                    return;
                }
            }
       }
       out.println("NO");
    }

    public int binarySearchIndex(long val , int start , int end , long[] arr){
        if(end - start <=1) {
            if(arr[end] <= val){
                return end;
            }
            else if(arr[start] <= val){
                return start;
            }
            else{
                return -1;
            }
        }
        int mid = (start + end + 1)/2;

        if(arr[mid] <= val){
            return binarySearchIndex(val,mid,end,arr);
        }
        else{
            return binarySearchIndex(val,start,mid,arr);
        }
    }


    public long[] fun(long n,int k,int a){
        long arr[]=new long[k];
        for(int i=0;i<k;i++){

            arr[(int)(pow(i, a, k)%k)]+=((n/k)%mod+ ((i!=0  &&  i<=n%k)? 1: 0))%mod;
        }
        return arr;
    }


    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;
    }
}

