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: Accepted)

/*input
2
5 1 1
100 1 1
*/
#include <bits/stdc++.h>
using namespace std;
const long long md=1e9+7;
long long a[1000005],n;

int main(){
	#ifdef ONLINE_JUDGE
	ios_base::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);
	#endif
	long long t,q,m,k,h,ans=0,sum=0,p,x,y,xold=0,yold=0,tlast=0;
	cin>>n;
	for(int i=0;i<n;++i){
		cin>>t>>x>>y;
		int moves = abs(x-xold) + abs(y-yold);
		if(moves>t-tlast || (t-tlast - moves)%2)
			return cout<<"No",0;
		tlast = t, xold = x, yold = y;
	}
	cout<<"Yes";
}