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: Wrong Answer)

#include <stdio.h>

int main()
{
    int n;
    scanf("%d",&n);
    
    int arr[n][3];
    for (int i = 0; i<n; i++){
        scanf("%d", &arr[i][0]);
        scanf("%d", &arr[i][1]);
        scanf("%d", &arr[i][2]);
    }
    
    int arr2[n][2];
    arr2[0][0] = arr[0][0];
    arr2[0][1] = arr[0][1] + arr[0][2];
    for (int k = 1; k<n; k++){
        arr2[k][0] = arr[k][0] - arr[k-1][0];
        arr2[k][1] = arr[k][1] - arr[k-1][1] + arr[k][2] - arr[k-1][2];
    }
    
    int c = 0;
    
    for (int j = 0; j<n; j++){
        if (arr2[j][1] <= arr2[j][0]){
            if (arr2[j][1]%2 == 0 && arr2[j][0]%2 == 0){
                c++;
            }
            else if (arr2[j][1]%2 != 0 && arr2[j][0]%2 != 0){
                c++;
            }
        }
    }
    
    if (c == 0){
        printf("No\n");
    }
    else {
        printf("Yes\n");
    }

    return 0;
}