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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

/// Created by ...Lusifer
#include<bits/stdc++.h>
using namespace std;
 
#define pb 		push_back
#define mp 		make_pair
#define prior   priority_queue
#define MOD 	1000000007
#define INF64 	(long long)1e18
#define INF 	(int)1e9
#define PI 		3.1415926535897932384626433832795 
#define ll      long long
#define ld		long double
#define ret     return
#define NUM 	1000001
const int SIZE = 2e5+4;
const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
void fastio(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
}

void solveTest(){
	int n;
	cin>>n;
	int t[n+1];
	int x[n+1],y[n+1];
	for(int i=0;i<n;i++){
		cin>>t[i]>>x[i]>>y[i];
	}
	int T0=0;
	int x0=0,y0=0;
	for(int i=0;i<n;i++){
		int T=t[i]-T0;
		int d=abs(x[i]-x0)+abs(y[i]-y0);
		if(d<=T&&d%2==T%2){
			continue;
		}
		else{
			cout<<"No"<<endl;
			return;
		}
		T0=t[i];
		x0=x[i];
		y0=y[i];
	}
	cout<<"Yes"<<endl;
	//cout<<endl<<"Time: "<<(float)clock()/CLOCKS_PER_SEC<<" seconds"<<endl;
	return ;
}
 
int main(){
	fastio();

	int t=1;
	//cin>>t;
	while(t--){
		solveTest();
 
	}
	return 0;
}