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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdlib>

int main(){
    int N = 0;
    std::cin >> N;
    int plans[N][3];
    for(int i = 0; i < N; i++){
        for(int j = 0; j < 3; j++){
            std::cin >> plans[i][j];
        }
    }
    bool answer = true;
    int t = plans[0][0];
    int a = plans[0][1];
    int b = plans[0][2];
    
    
    for(int i = 0; i < N; i++){
        if(i != 0){
            t = std::abs(plans[i - 1][0] - t);
            a = std::abs(plans[i - 1][1] - a);
            b = std::abs(plans[i - 1][2] - b);
        }
        int cost = a + b;
        if(!(cost <= t && (cost - t) % 2 == 0)){
            answer = false;
            break;
        }
    }
    if(answer){
        std::cout << "Yes";
    }else{
        std::cout << "No";
    }
}