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 <string>
#include <vector>
#include <algorithm>
#include <stdlib.h>
using namespace std;

int main(){

  int N;
  cin >> N;
  vector<int> t_vector(N);
  vector<int> x_vector(N);
  vector<int> y_vector(N);

  for(int i=0;i<N;++i){
    cin >> t_vector[i] >> x_vector[i] >> y_vector[i];
  }

  int t_now;
  int t_next;
  int x_now;
  int y_now;
  int x_next;
  int y_next;
  bool flag = true;

  t_next = 0;
  x_next = 0;
  y_next = 0;

  for(int i=0; i<N; ++i){
    t_now = t_next;
    x_now = x_next;
    y_now = y_next;

    t_next = t_vector[i];
    x_next = x_vector[i];
    y_next = y_vector[i];

    int x_sa = abs(x_next - x_now);
    int y_sa = abs(y_next - y_now);
    int t_sa = t_next - t_now;

    if (x_sa + y_sa % 2 != t_sa % 2){
      flag = false;
      cout << "No" << endl;
      break;
    } else if(x_sa + y_sa > t_sa){
      flag = false;
      cout << "No" << endl;
      break;
    }
  }

  if (flag){
    cout << "Yes" << endl;
  }


  return 0;
}