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 <math.h>

int main(){

    int N, i;
    scanf("%d", &N);
    //printf("N:%d", N);

    const int MAX = N+1;
    int ti[MAX], xi[MAX], yi[MAX]; // i=0にt=0の条件:(x,y)=(0,0)を格納しないとN=1の処理が出来ない
    char dammy;

    // 配列初期化, t=0の条件を追加
    for (i = 0; i < N;i++){
        ti[i] = xi[i] = yi[i] = 0;
    }

    for (i = 1; i < MAX; i++)
    {
        scanf("%c", &dammy);
        scanf("%d %d %d", &ti[i], &xi[i], &yi[i]);
        
    }

    int distance = 0;
    int judge = 1;
 
    for (i = 0; i < MAX-1; i++){
        distance = abs(xi[i + 1] - xi[i]) + abs(yi[i + 1] - yi[i]);
        if((distance <= abs((ti[i+1]-ti[i]))&&(distance%2 == abs((ti[i+1]-ti[i]))%2))){
            judge *= 1;
        }else{
            judge *= 0;
        }
    }

    if(judge == 1){
        printf("Yes");
    }else{
        printf("No");
    }

        return 0;
}