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>
#include <stdlib.h>

int saitan(int x,int y ,int xx,int yy);
int check(int d, int tt);

int main(void){
	int n = 0, i = 0;
	int *x, *y, *t;
	x = calloc(100000, sizeof(int ));
	y = calloc(100000, sizeof(int ));
	t = calloc(100000, sizeof(int ));
	if(x == NULL||y == NULL||t == NULL)exit(0);
	
	scanf("%d",&n);
	
	t[0] = 0; x[0] = 0; y[0] = 0;
	for(i=1;i<=n;i++){
		scanf("%d %d %d",&t[i], &x[i], &y[i]);
	}
	
	int d = 0, tt = 0, a = 0;
	
	for(i=0;i<n;i++){
		d = saitan(x[i], y[i], x[i+1], y[i+1]);
		tt = t[i+1] - t[i];
		
		a = check(d, tt);
		if(a == 0){
			printf("No");
			free(x);free(y);free(t);
			return 0;
			}
	}
	printf("Yes");
	free(x);free(y);free(t);
	return 0;
}

int saitan(int x,int y ,int xx,int yy){
	int d = 0;
	d += abs(xx - x);
	d += abs(yy - y);
	
	return d;
}

int check(int d, int tt){
	if(tt >= d){
		if(tt % 2 == d % 2) return 1;
		}
	return 0;
}