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)

#include <bits/stdc++.h>
using namespace std;

/*
到達できないケースは、次の2通り
1.必要移動距離が長くて、時間が足りない場合。
2.余った時間が、奇数の場合。

方針は、全予定に対して、上の条件に抵触しないかどうかチェックすればよい。
*/


int main(){
	int n;
	cin >> n;
	
	bool flag = true;
	int st = 0, sx = 0, sy = 0;
	for(int i=0; i<n; i++){
		int t, x, y;
		cin >> t >> x >> y;
		int d = (x - sx) + (y - sy);
		if(t - st < d) flag = false;
		else if(t - st != d && (t - st - d) % 2) flag = false;
	}
	
	if(flag) cout << "Yes" << endl;
	else cout << "No" << endl;
	
	return 0;
}