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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int abs(int a);

int main(void)
{
	int n, t, x, y, tt, xx, yy;
	int i;

	scanf("%d%*c", &n);

	t = 0; x = 0; y = 0;

	for(i=0;i<n;i++) {
		int dist, dt;

		scanf("%d %d %d%*c", &tt, &xx, &yy);
		dist = abs(xx-x) + abs(yy-y);
		dt = tt - t;

		if(dist > dt) {
			printf("No\n");
			return 0;
		} else if((dt - dist) % 2) {
			printf("No\n");
			return 0;
		}

		t = tt; x = xx; y = yy;
	}

	printf("Yes\n");
	
	return 0;
}

int abs(int a)
{
	if(a) return a;
	return -a;
}