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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<string>
#include<cmath>
#define ll long long
#define INF 0x3f3f3f3f
#define N 1005
using namespace std;



int main()
{
	ll n,t,x,y,nt=0,nx=0,ny=0;
	bool flag=true;
	cin>>n;
	for(int i=1;i<=n;i++){
		cin>>t>>x>>y;
		if(!flag) continue;
		ll len=abs(x-nx)+abs(y-ny);
		ll x=abs(t-nt);
		
		if(x>=len){
			if(len%2==0){
				if(x%2==0);else flag=false;
			}else{
				if(x%2==1) ;else flag=false;
			}
		}else flag=false;
		
		if(len>t-nt||(len%2==0)&&(x%2)||(len%2)&&(x%2==0)){
			flag=false;
			continue;
		}
		nt=t;
		nx=x;
		ny=y;
	}
	if(flag)
	puts("Yes");
	else puts("No");
	return 0;
}