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>
#include <string.h>
#include <math.h>

/*ソートの時に使う
int sort(const void *a, const void *b){
    return *(int*)a-*(int*)b ;
}
    qsort (data,sizeof(data),sizeof(int),sort); 
*/

int main(void){
    int n;
    scanf("%d",&n);
    int t[n],x[n],y[n];
    for (int i=0; i<n; i++){
        scanf("%d%d%d",&t[i],&x[i],&y[i]);
    }
    
    for (int i=0; i<n; i++){
        if(i==0 && t[i]>=(x[i]+y[i]) && (t[i]-(x[i]+y[i]))%2==0 ){
            
        } else if ( (t[i]-t[i-1]) >= (abs(x[i]-x[i-1])+abs(y[i]-y[i-1])) && ( (t[i]-t[i-1])-( abs(x[i]-x[i-1])+abs(y[i]-y[i-1]) ) )%2==0 ){
            
        } else {
            printf("No\n");
            exit (0) ;
        }
    }
    printf ("Yes\n");
	return 0 ;
}