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: Wrong Answer)

#include <iostream>
#include <cstdlib>
#include <algorithm>
using namespace std;

#define LEN 3
#define T 0
#define X 1
#define Y 2
#define X_NG 0
#define Y_NG 1
#define ALL_OK 2

int main(void){
    int N;
    cin >> N;
    int travelplan[N][LEN];
    for(int i = 0; i < N; i++){
        for(int j = 0; j < LEN; j++){
            cin >> travelplan[i][j];
        } 
    }

    int location[LEN] ={0,0,0};
    int tmp = 0;
    bool possbleflg = false;
    int state = X_NG; 
    for(int i = 0; i < N; i++){
        for(int j = location[T]; j <= travelplan[i][T]; ++j){
            switch(state){
                case X_NG:
                    tmp = travelplan[i][X] - location[X];
                    if(tmp == 0) {
                        state = Y_NG;
                    }
                    else if(tmp > 0){
                        location[X] += 1;
                        break;
                    }
                    else  if(tmp < 0){
                        location[X] -= 1; 
                        break;   
                    }
                case Y_NG:
                    tmp = travelplan[i][Y] - location[Y];
                    if(tmp == 0) {
                        state = ALL_OK;
                    }
                    else if(tmp > 0){
                        location[Y] += 1;
                        break;
                    }
                    else  if(tmp < 0){
                        location[Y] -= 1; 
                        break;   
                    }
                case ALL_OK:                
                    if(j != travelplan[i][T]){
                         location[Y] += 1;
                         state = Y_NG;
                    }else{
                        
                        possbleflg = true;
                        location[T] = travelplan[i][T];
                        location[X] = travelplan[i][X];
                        location[Y] = travelplan[i][Y];
                    }
                default:
                    break;
            }
        }
        if(possbleflg == false) break;
    }

    if(possbleflg == true){
      cout << "Yes" << endl;
    }else{
       cout << "No" << endl;       
    }

    return 0;
}