Problem:
Score : 300 points

Problem Statement

AtCoDeer the deer is going on a trip in a two-dimensional plane.
In his plan, he will depart from point (0, 0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i,y_i) at time t_i.

If AtCoDeer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1,y), (x-1,y), (x,y+1) and (x,y-1).
Note that he cannot stay at his place.
Determine whether he can carry out his plan.

Constraints

1 ≤ N ≤ 10^5

0 ≤ x_i ≤ 10^5

0 ≤ y_i ≤ 10^5

1 ≤ t_i ≤ 10^5

t_i < t_{i+1} (1 ≤ i ≤ N-1)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
t_1 x_1 y_1
t_2 x_2 y_2
:
t_N x_N y_N

Output

If AtCoDeer can carry out his plan, print Yes; if he cannot, print No.

Sample Input 1

2
3 1 2
6 1 1

Sample Output 1

Yes

For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).

Sample Input 2

1
2 100 100

Sample Output 2

No

It is impossible to be at (100,100) two seconds after being at (0,0).

Sample Input 3

2
5 1 1
100 1 1

Sample Output 3

No

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;
import java.math.BigInteger;
public class Main {
    private static StringBuilder sb = new StringBuilder();
    private static void s(String s){
        System.out.print(s);
    }
    private static void s(Double s){
        System.out.print(s);
    }
    private static void s(char s){
        System.out.print(s);
    }
    private static void sn(String s){
        System.out.println(s);
    }
    private static void sn(Boolean s){
        System.out.println(s);
    }
    private static void sn(long s){
        System.out.println(s);
    }
    private static void sn(Double s){
        System.out.println(s);
    }
    private static void sn(String s, Object o){
        sb.append(s+"\n");
    }
    private static void sn(long s, Object o){
        sb.append(s+"\n");
    }
    private static void sn(boolean s, Object o){
        sb.append(s+"\n");
    }
    private static void pr() throws Exception{
        BufferedWriter bw =new BufferedWriter(new OutputStreamWriter(System.out));
        bw.write(sb.toString());
        bw.flush();
    }
    static class Reader{
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
    private static boolean isPrime(Integer ii){
        return new BigInteger(ii+"").isProbablePrime(1);
    }
    private static boolean isDigit(int ii){
        return Character.isDigit((char)ii);
    }
    private static long fact(int f){
        if(f==0){
            return 1;
        }
        return (long)f * (long)fact(f-1);
    }
    /*static int ar[] = new int[1000000];
    static {
        Arrays.fill(ar, 1000070);
        ar[0]=0;
        int arrr[] = new int[]{2,3,5,7};
        for(int i=0;i<4;i++){
            for(int ii=0;ii<1000000;ii++){
                if(ii>=arrr[i]){
                    ar[ii] = Math.min(ar[ii], 1+ar[ii-arrr[i]]);
                }
            }
        }
    }*/
    /*static{
        Arrays.fill(prime, true);
        for(int p = 2; p*p <=1000070; p++)
        {
            // If prime[p] is not changed, then it is a prime
            if(prime[p] == true)
            {
                // Update all multiples of p
                for(int i = p*2; i <= 1000070; i += p)
                    prime[i] = false;
            }
        }
        int nc = 0;
        for(int p = 2; p <=1000070; p++)
        {
            if(prime[p] == true && prime[(p+1)/2] == true)
            {
                prr[p]+=nc+1;
                nc = prr[p];
            }
        }
    }*/
    private static Reader r = new Reader();
    private static int ni() throws Exception{
        return r.nextInt();
    }
    private static long nl() throws Exception{
        return r.nextLong();
    }
    private static int[] na(int a) throws Exception{
        int arr[] = new int[a];
        for(int i=0;i<a;i++){
            arr[i] = r.nextInt();
        }
        return arr;
    }
    private static boolean isSquare(int a){
        double sqt = Math.sqrt(a);
        return (int)sqt == sqt;
    }
    private static int lSquare(int a){
        double sqt = Math.sqrt(a);
        return (int)sqt * (int) sqt;
    }
    private static int rSquare(int a){
        double sqt = Math.sqrt(a);
        return (int)Math.ceil(sqt) * (int)Math.ceil(sqt);
    }
    private static int parent[] = new int[200005];
    private static boolean visit[] = new boolean[200005];
    private static void init(){
    	for(int i=0;i<200005;i++){
    		parent[i] = 0;
    	}
    	for(int i=0;i<200005;i++){
    		visit[i] = false;
    	}
    }
	private static void bfs(int size[], int ans, List[] list, int start, int end, Queue<Integer> q){
    	while(!q.isEmpty()){
    		int temp = q.remove();
    		visit[temp] = true;
    		for(int i=0;i<list[temp].size();i++){
    			if(!visit[(int)list[temp].get(i)] && end == (int)list[temp].get(i)){
    				parent[end] = temp;
    				visit[(int)list[temp].get(i)] = true;
    				return;
    			}
    			if(!visit[(int)list[temp].get(i)]){
    				q.add((int)list[temp].get(i));
    				parent[(int)list[temp].get(i)] = temp;
    			}
    		}
    	}
    }
    public static int dfs(List []list, int arr[], int k, int i, int ii){
        if(i==1 && arr[i]!=arr[ii]){
            return -1;
        }
        if(arr[i] == arr[ii]){
            k--;
            if(k==0){
                return i;
            }
        }
        for(int j=0;j<list[i].size();j++){
            return dfs(list, arr, k, (int)list[i].get(j), ii);
        }
        return -1;
        }
        private static boolean isPerfectSquare(int n){
            if((int)Math.sqrt(n) * (int)Math.sqrt(n) == n){
                return true;
            }
            return false;
        }
        
        private static boolean cany(int n, int nn, int t){
            if(n>t || t<0 || n<0 || nn>t || nn<0){
                return false;
            }
            if(n == 0 && t==0 && nn==0){
                return true;
            }
            return cany(n-1,nn, t-1) || cany(n+1,nn, t-1) || cany(n,nn-1, t-1) || cany(n,nn + 1, t-1);
        }
	public static void main (String[] args) throws Exception{
	    int n = ni();
	    while(n-->0){
	        int t = ni();
	        int x = ni();
	        int y = ni();
	        if(!cany(x, y, t)){
	            sn("No");
	            return;
	        }
	    }
	    sn("Yes");
	}
}