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 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(void){
    int n;
    int nowX = 0,nowY = 0,count = 0;

    scanf("%d\n",&n);
    int time[n];
    int x[n];
    int y[n];
    for (int k = 0; k < n; ++k) {
        scanf("%d %d %d",&time[k],&x[k],&y[k]);
    }

    for (int i = 0; i < n; ++i) {
        count = 0;
        for (int j = 0; j < time[i]; ++j) {
            count++;
            if (x[i] > nowX){
                nowX += 1;
                continue;
            }
            else if(x[i] < nowX){
                nowX -= 1;
                continue;
            }
            else if(y[i] > nowY){
                nowY += 1;
                continue;
            }
            else if(y[i] <= nowY){
                nowY -= 1;
            }
        }
        if (nowX != x[i] || nowY != y[i]){
            printf("No");
            return 0;
        }
    }
    printf("Yes");
    return 0;
}