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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Linq;
using System.Numerics;

namespace AtCoderWorkspace
{
    class Program
    {
        static void Main(string[] args)
        {
            var cin = new Scanner();
            var n = cin.nextInt();
            var list = new List<Point>();
            for (int i = 0; i < n; i++)
            {
                list.Add(new Point()
                {
                    t = cin.nextInt(),
                    x = cin.nextInt(),
                    y = cin.nextInt(),
                });
            }

            var p = new Point() { x=0, y = 0, t = 0};
            for (int i = 0; i < n; i++)
            {
                var dist = Math.Abs(list[i].x - p.x) + Math.Abs(list[i].y - p.y);
                var dt = list[i].t - p.t;
                if(dist > dt)
                {
                    Console.WriteLine("No");
                    return;
                }

                if(dist % 2 != dt % 2)
                {
                    Console.WriteLine("No");
                    return;
                }

                p = list[i];
            }

            Console.WriteLine("Yes");
        }
    }

    class Point
    {
        public int x { get; set; }
        public int y { get; set; }
        public int t { get; set; }
    }



    static class C
    {
        public static long LowerBound(long[] a, long key)
        {
            long l = 0;
            long r = a.Length;
            long mid;
            while (l < r)
            {
                mid = ((r - l) / 2) + l;
                if (a[mid] <= key)
                    l = mid + 1;
                else
                    r = mid;
            }
            return l;
        }

        public static long UpperBound(long[] a, long key)
        {
            long l = 0;
            long r = a.Length;
            long mid;
            while (l < r)
            {
                mid = ((r - l) / 2) + l;
                if (a[mid] < key)
                    l = mid + 1;
                else
                    r = mid;
            }
            return l;
        }
    }

    static class Subsequence
    {
       /// <summary>
       /// 最長増加部分列
       /// </summary>
       /// <param name="a">long[]</param>
       /// <returns></returns>
        public static long LIS(long[] a)
        {
            var dp = Enumerable.Range(0, a.Length).Select(x => long.MaxValue).ToArray();
            for (int i = 0; i < a.Length; i++)
            {
                dp[C.LowerBound(dp, a[i])] = a[i];
            }
            return C.LowerBound(dp, long.MaxValue-1);
        }

        /// <summary>
        /// 重複を許さない最長増加部分列
        /// </summary>
        /// <param name="a">long[]</param>
        /// <returns></returns>
        public static long UniqueLIS(long[] a)
        {
            var dp = Enumerable.Range(0, a.Length).Select(x => long.MaxValue).ToArray();
            for (int i = 0; i < a.Length; i++)
            {
                dp[C.UpperBound(dp, a[i])] = a[i];
            }
            return C.UpperBound(dp, long.MaxValue - 1);
        }
    }

    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt() + add;
            }
            return Array;
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong() + add;
            }
            return Array;
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextDouble() + add;
            }
            return Array;
        }
    }

    #region ModInt

    public class ModInt
    {
        public static long Mod;

        public long num;

        public ModInt(long n, int mod = (int)1e9 + 7) { num = n; Mod = mod; }        
        public override string ToString() { return num.ToString(); }
        public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
        public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
        public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
        public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }
        public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }
        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
                if ((k & 1) == 1) ret = ret * v % Mod;
            return new ModInt(ret);
        }
        public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
    }
    #endregion
}